Construction of singular limits for a strongly perturbed four-dimensional Navier problem with exponentially dominated nonlinearity and nonlinear terms
Abstract Given a bounded open regular set Ω∈R4,x1,x2,…,xm∈Ω,λ,ρ<0,γ∈(0,1) $\varOmega \in \mathbb{R}^{4}, x_{1}, x_{2}, \ldots, x_{m} \in \varOmega, \lambda, \rho < 0, \gamma \in (0,1)$, and Qλ ${\mathscr{Q}}_{\lambda }$ some nonlinear operator (which will be defined later), we prove that the p...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Sami Baraket [verfasserIn] Souhail Chebbi [verfasserIn] Nejmeddine Chorfi [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2019 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
In: Boundary Value Problems - SpringerOpen, 2006, (2019), 1, Seite 25 |
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| Übergeordnetes Werk: |
year:2019 ; number:1 ; pages:25 |
| Links: |
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| DOI / URN: |
10.1186/s13661-019-1244-7 |
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| Katalog-ID: |
DOAJ035529385 |
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| 520 | |a Abstract Given a bounded open regular set Ω∈R4,x1,x2,…,xm∈Ω,λ,ρ<0,γ∈(0,1) $\varOmega \in \mathbb{R}^{4}, x_{1}, x_{2}, \ldots, x_{m} \in \varOmega, \lambda, \rho < 0, \gamma \in (0,1)$, and Qλ ${\mathscr{Q}}_{\lambda }$ some nonlinear operator (which will be defined later), we prove that the problem Δ2u+Qλ(u)=ρ4(eu+eγu) $$ \Delta ^{2}u +{\mathscr{Q}}_{\lambda }(u)= \rho ^{4} \bigl(e^{u} + e^{\gamma u}\bigr) $$ has a positive weak solution in Ω with u=Δu=0 $u = \Delta u=0$ on ∂Ω, which is singular at each xi $x_{i}$ as the parameters λ and ρ tend to 0. | ||
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10.1186/s13661-019-1244-7 doi (DE-627)DOAJ035529385 (DE-599)DOAJ39899e0787ae4eca9c39f66ad05a70c4 DE-627 ger DE-627 rakwb eng QA299.6-433 Sami Baraket verfasserin aut Construction of singular limits for a strongly perturbed four-dimensional Navier problem with exponentially dominated nonlinearity and nonlinear terms 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Given a bounded open regular set Ω∈R4,x1,x2,…,xm∈Ω,λ,ρ<0,γ∈(0,1) $\varOmega \in \mathbb{R}^{4}, x_{1}, x_{2}, \ldots, x_{m} \in \varOmega, \lambda, \rho < 0, \gamma \in (0,1)$, and Qλ ${\mathscr{Q}}_{\lambda }$ some nonlinear operator (which will be defined later), we prove that the problem Δ2u+Qλ(u)=ρ4(eu+eγu) $$ \Delta ^{2}u +{\mathscr{Q}}_{\lambda }(u)= \rho ^{4} \bigl(e^{u} + e^{\gamma u}\bigr) $$ has a positive weak solution in Ω with u=Δu=0 $u = \Delta u=0$ on ∂Ω, which is singular at each xi $x_{i}$ as the parameters λ and ρ tend to 0. Biharmonic operator Nonlinear operator Singular limits Green’s function Nonlinear domain decomposition method Analysis Souhail Chebbi verfasserin aut Nejmeddine Chorfi verfasserin aut In Boundary Value Problems SpringerOpen, 2006 (2019), 1, Seite 25 (DE-627)48672557X (DE-600)2187777-4 16872770 nnns year:2019 number:1 pages:25 https://doi.org/10.1186/s13661-019-1244-7 kostenfrei https://doaj.org/article/39899e0787ae4eca9c39f66ad05a70c4 kostenfrei http://link.springer.com/article/10.1186/s13661-019-1244-7 kostenfrei https://doaj.org/toc/1687-2770 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2019 1 25 |
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10.1186/s13661-019-1244-7 doi (DE-627)DOAJ035529385 (DE-599)DOAJ39899e0787ae4eca9c39f66ad05a70c4 DE-627 ger DE-627 rakwb eng QA299.6-433 Sami Baraket verfasserin aut Construction of singular limits for a strongly perturbed four-dimensional Navier problem with exponentially dominated nonlinearity and nonlinear terms 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Given a bounded open regular set Ω∈R4,x1,x2,…,xm∈Ω,λ,ρ<0,γ∈(0,1) $\varOmega \in \mathbb{R}^{4}, x_{1}, x_{2}, \ldots, x_{m} \in \varOmega, \lambda, \rho < 0, \gamma \in (0,1)$, and Qλ ${\mathscr{Q}}_{\lambda }$ some nonlinear operator (which will be defined later), we prove that the problem Δ2u+Qλ(u)=ρ4(eu+eγu) $$ \Delta ^{2}u +{\mathscr{Q}}_{\lambda }(u)= \rho ^{4} \bigl(e^{u} + e^{\gamma u}\bigr) $$ has a positive weak solution in Ω with u=Δu=0 $u = \Delta u=0$ on ∂Ω, which is singular at each xi $x_{i}$ as the parameters λ and ρ tend to 0. Biharmonic operator Nonlinear operator Singular limits Green’s function Nonlinear domain decomposition method Analysis Souhail Chebbi verfasserin aut Nejmeddine Chorfi verfasserin aut In Boundary Value Problems SpringerOpen, 2006 (2019), 1, Seite 25 (DE-627)48672557X (DE-600)2187777-4 16872770 nnns year:2019 number:1 pages:25 https://doi.org/10.1186/s13661-019-1244-7 kostenfrei https://doaj.org/article/39899e0787ae4eca9c39f66ad05a70c4 kostenfrei http://link.springer.com/article/10.1186/s13661-019-1244-7 kostenfrei https://doaj.org/toc/1687-2770 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2019 1 25 |
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10.1186/s13661-019-1244-7 doi (DE-627)DOAJ035529385 (DE-599)DOAJ39899e0787ae4eca9c39f66ad05a70c4 DE-627 ger DE-627 rakwb eng QA299.6-433 Sami Baraket verfasserin aut Construction of singular limits for a strongly perturbed four-dimensional Navier problem with exponentially dominated nonlinearity and nonlinear terms 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Given a bounded open regular set Ω∈R4,x1,x2,…,xm∈Ω,λ,ρ<0,γ∈(0,1) $\varOmega \in \mathbb{R}^{4}, x_{1}, x_{2}, \ldots, x_{m} \in \varOmega, \lambda, \rho < 0, \gamma \in (0,1)$, and Qλ ${\mathscr{Q}}_{\lambda }$ some nonlinear operator (which will be defined later), we prove that the problem Δ2u+Qλ(u)=ρ4(eu+eγu) $$ \Delta ^{2}u +{\mathscr{Q}}_{\lambda }(u)= \rho ^{4} \bigl(e^{u} + e^{\gamma u}\bigr) $$ has a positive weak solution in Ω with u=Δu=0 $u = \Delta u=0$ on ∂Ω, which is singular at each xi $x_{i}$ as the parameters λ and ρ tend to 0. Biharmonic operator Nonlinear operator Singular limits Green’s function Nonlinear domain decomposition method Analysis Souhail Chebbi verfasserin aut Nejmeddine Chorfi verfasserin aut In Boundary Value Problems SpringerOpen, 2006 (2019), 1, Seite 25 (DE-627)48672557X (DE-600)2187777-4 16872770 nnns year:2019 number:1 pages:25 https://doi.org/10.1186/s13661-019-1244-7 kostenfrei https://doaj.org/article/39899e0787ae4eca9c39f66ad05a70c4 kostenfrei http://link.springer.com/article/10.1186/s13661-019-1244-7 kostenfrei https://doaj.org/toc/1687-2770 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2019 1 25 |
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10.1186/s13661-019-1244-7 doi (DE-627)DOAJ035529385 (DE-599)DOAJ39899e0787ae4eca9c39f66ad05a70c4 DE-627 ger DE-627 rakwb eng QA299.6-433 Sami Baraket verfasserin aut Construction of singular limits for a strongly perturbed four-dimensional Navier problem with exponentially dominated nonlinearity and nonlinear terms 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Given a bounded open regular set Ω∈R4,x1,x2,…,xm∈Ω,λ,ρ<0,γ∈(0,1) $\varOmega \in \mathbb{R}^{4}, x_{1}, x_{2}, \ldots, x_{m} \in \varOmega, \lambda, \rho < 0, \gamma \in (0,1)$, and Qλ ${\mathscr{Q}}_{\lambda }$ some nonlinear operator (which will be defined later), we prove that the problem Δ2u+Qλ(u)=ρ4(eu+eγu) $$ \Delta ^{2}u +{\mathscr{Q}}_{\lambda }(u)= \rho ^{4} \bigl(e^{u} + e^{\gamma u}\bigr) $$ has a positive weak solution in Ω with u=Δu=0 $u = \Delta u=0$ on ∂Ω, which is singular at each xi $x_{i}$ as the parameters λ and ρ tend to 0. Biharmonic operator Nonlinear operator Singular limits Green’s function Nonlinear domain decomposition method Analysis Souhail Chebbi verfasserin aut Nejmeddine Chorfi verfasserin aut In Boundary Value Problems SpringerOpen, 2006 (2019), 1, Seite 25 (DE-627)48672557X (DE-600)2187777-4 16872770 nnns year:2019 number:1 pages:25 https://doi.org/10.1186/s13661-019-1244-7 kostenfrei https://doaj.org/article/39899e0787ae4eca9c39f66ad05a70c4 kostenfrei http://link.springer.com/article/10.1186/s13661-019-1244-7 kostenfrei https://doaj.org/toc/1687-2770 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2019 1 25 |
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10.1186/s13661-019-1244-7 doi (DE-627)DOAJ035529385 (DE-599)DOAJ39899e0787ae4eca9c39f66ad05a70c4 DE-627 ger DE-627 rakwb eng QA299.6-433 Sami Baraket verfasserin aut Construction of singular limits for a strongly perturbed four-dimensional Navier problem with exponentially dominated nonlinearity and nonlinear terms 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Given a bounded open regular set Ω∈R4,x1,x2,…,xm∈Ω,λ,ρ<0,γ∈(0,1) $\varOmega \in \mathbb{R}^{4}, x_{1}, x_{2}, \ldots, x_{m} \in \varOmega, \lambda, \rho < 0, \gamma \in (0,1)$, and Qλ ${\mathscr{Q}}_{\lambda }$ some nonlinear operator (which will be defined later), we prove that the problem Δ2u+Qλ(u)=ρ4(eu+eγu) $$ \Delta ^{2}u +{\mathscr{Q}}_{\lambda }(u)= \rho ^{4} \bigl(e^{u} + e^{\gamma u}\bigr) $$ has a positive weak solution in Ω with u=Δu=0 $u = \Delta u=0$ on ∂Ω, which is singular at each xi $x_{i}$ as the parameters λ and ρ tend to 0. Biharmonic operator Nonlinear operator Singular limits Green’s function Nonlinear domain decomposition method Analysis Souhail Chebbi verfasserin aut Nejmeddine Chorfi verfasserin aut In Boundary Value Problems SpringerOpen, 2006 (2019), 1, Seite 25 (DE-627)48672557X (DE-600)2187777-4 16872770 nnns year:2019 number:1 pages:25 https://doi.org/10.1186/s13661-019-1244-7 kostenfrei https://doaj.org/article/39899e0787ae4eca9c39f66ad05a70c4 kostenfrei http://link.springer.com/article/10.1186/s13661-019-1244-7 kostenfrei https://doaj.org/toc/1687-2770 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2019 1 25 |
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Construction of singular limits for a strongly perturbed four-dimensional Navier problem with exponentially dominated nonlinearity and nonlinear terms |
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Abstract Given a bounded open regular set Ω∈R4,x1,x2,…,xm∈Ω,λ,ρ<0,γ∈(0,1) $\varOmega \in \mathbb{R}^{4}, x_{1}, x_{2}, \ldots, x_{m} \in \varOmega, \lambda, \rho < 0, \gamma \in (0,1)$, and Qλ ${\mathscr{Q}}_{\lambda }$ some nonlinear operator (which will be defined later), we prove that the problem Δ2u+Qλ(u)=ρ4(eu+eγu) $$ \Delta ^{2}u +{\mathscr{Q}}_{\lambda }(u)= \rho ^{4} \bigl(e^{u} + e^{\gamma u}\bigr) $$ has a positive weak solution in Ω with u=Δu=0 $u = \Delta u=0$ on ∂Ω, which is singular at each xi $x_{i}$ as the parameters λ and ρ tend to 0. |
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Abstract Given a bounded open regular set Ω∈R4,x1,x2,…,xm∈Ω,λ,ρ<0,γ∈(0,1) $\varOmega \in \mathbb{R}^{4}, x_{1}, x_{2}, \ldots, x_{m} \in \varOmega, \lambda, \rho < 0, \gamma \in (0,1)$, and Qλ ${\mathscr{Q}}_{\lambda }$ some nonlinear operator (which will be defined later), we prove that the problem Δ2u+Qλ(u)=ρ4(eu+eγu) $$ \Delta ^{2}u +{\mathscr{Q}}_{\lambda }(u)= \rho ^{4} \bigl(e^{u} + e^{\gamma u}\bigr) $$ has a positive weak solution in Ω with u=Δu=0 $u = \Delta u=0$ on ∂Ω, which is singular at each xi $x_{i}$ as the parameters λ and ρ tend to 0. |
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Abstract Given a bounded open regular set Ω∈R4,x1,x2,…,xm∈Ω,λ,ρ<0,γ∈(0,1) $\varOmega \in \mathbb{R}^{4}, x_{1}, x_{2}, \ldots, x_{m} \in \varOmega, \lambda, \rho < 0, \gamma \in (0,1)$, and Qλ ${\mathscr{Q}}_{\lambda }$ some nonlinear operator (which will be defined later), we prove that the problem Δ2u+Qλ(u)=ρ4(eu+eγu) $$ \Delta ^{2}u +{\mathscr{Q}}_{\lambda }(u)= \rho ^{4} \bigl(e^{u} + e^{\gamma u}\bigr) $$ has a positive weak solution in Ω with u=Δu=0 $u = \Delta u=0$ on ∂Ω, which is singular at each xi $x_{i}$ as the parameters λ and ρ tend to 0. |
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Construction of singular limits for a strongly perturbed four-dimensional Navier problem with exponentially dominated nonlinearity and nonlinear terms |
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