Note on a discrete initial value problem from a competition

Abstract The following discrete initial value problem xn+1=xn(xn−12−2)−x1,n∈N,%$ x_{n+1}=x_{n}\bigl(x_{n-1}^{2}-2 \bigr)-x_{1},\quad n\in {\mathbb{N}}, %%$x_{0}=2$ and $x_{1}=5/2$, appeared at an international competition. It is known that the problem can be solved in closed form. Here we discuss th...
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Autor*in:	Stević, Stevo [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2021

Schlagwörter:	Discrete initial value problem Nonlinear difference equation Closed-form formula Solvable equation

Übergeordnetes Werk:	Enthalten in: Advances in difference equations - [S.l.] : Springer International, 2004, 2021(2021), 1 vom: 30. Jan.
Übergeordnetes Werk:	volume:2021 ; year:2021 ; number:1 ; day:30 ; month:01

Links:	Volltext

DOI / URN:	10.1186/s13662-021-03251-w

Katalog-ID:	SPR042943671

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520			\|a Abstract The following discrete initial value problem xn+1=xn(xn−12−2)−x1,n∈N,%$ x_{n+1}=x_{n}\bigl(x_{n-1}^{2}-2 \bigr)-x_{1},\quad n\in {\mathbb{N}}, %%$x_{0}=2$ and $x_{1}=5/2$, appeared at an international competition. It is known that the problem can be solved in closed form. Here we discuss the solvability of a more general initial value problem which includes the former one. We show that, in a sense, there are not so many solvable discrete initial value problems related to this one, showing its specificity, which is a bit surprising result.
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spelling	10.1186/s13662-021-03251-w doi (DE-627)SPR042943671 (DE-599)SPRs13662-021-03251-w-e (SPR)s13662-021-03251-w-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Stević, Stevo verfasserin aut Note on a discrete initial value problem from a competition 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The following discrete initial value problem xn+1=xn(xn−12−2)−x1,n∈N,%$ x_{n+1}=x_{n}\bigl(x_{n-1}^{2}-2 \bigr)-x_{1},\quad n\in {\mathbb{N}}, %%$x_{0}=2$ and $x_{1}=5/2$, appeared at an international competition. It is known that the problem can be solved in closed form. Here we discuss the solvability of a more general initial value problem which includes the former one. We show that, in a sense, there are not so many solvable discrete initial value problems related to this one, showing its specificity, which is a bit surprising result. Discrete initial value problem (dpeaa)DE-He213 Nonlinear difference equation (dpeaa)DE-He213 Closed-form formula (dpeaa)DE-He213 Solvable equation (dpeaa)DE-He213 Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2021(2021), 1 vom: 30. Jan. (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2021 year:2021 number:1 day:30 month:01 https://dx.doi.org/10.1186/s13662-021-03251-w kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE 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_74 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 31.49 ASE AR 2021 2021 1 30 01
allfields_unstemmed	10.1186/s13662-021-03251-w doi (DE-627)SPR042943671 (DE-599)SPRs13662-021-03251-w-e (SPR)s13662-021-03251-w-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Stević, Stevo verfasserin aut Note on a discrete initial value problem from a competition 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The following discrete initial value problem xn+1=xn(xn−12−2)−x1,n∈N,%$ x_{n+1}=x_{n}\bigl(x_{n-1}^{2}-2 \bigr)-x_{1},\quad n\in {\mathbb{N}}, %%$x_{0}=2$ and $x_{1}=5/2$, appeared at an international competition. It is known that the problem can be solved in closed form. Here we discuss the solvability of a more general initial value problem which includes the former one. We show that, in a sense, there are not so many solvable discrete initial value problems related to this one, showing its specificity, which is a bit surprising result. Discrete initial value problem (dpeaa)DE-He213 Nonlinear difference equation (dpeaa)DE-He213 Closed-form formula (dpeaa)DE-He213 Solvable equation (dpeaa)DE-He213 Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2021(2021), 1 vom: 30. Jan. (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2021 year:2021 number:1 day:30 month:01 https://dx.doi.org/10.1186/s13662-021-03251-w kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE 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_74 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 31.49 ASE AR 2021 2021 1 30 01
allfieldsGer	10.1186/s13662-021-03251-w doi (DE-627)SPR042943671 (DE-599)SPRs13662-021-03251-w-e (SPR)s13662-021-03251-w-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Stević, Stevo verfasserin aut Note on a discrete initial value problem from a competition 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The following discrete initial value problem xn+1=xn(xn−12−2)−x1,n∈N,%$ x_{n+1}=x_{n}\bigl(x_{n-1}^{2}-2 \bigr)-x_{1},\quad n\in {\mathbb{N}}, %%$x_{0}=2$ and $x_{1}=5/2$, appeared at an international competition. It is known that the problem can be solved in closed form. Here we discuss the solvability of a more general initial value problem which includes the former one. We show that, in a sense, there are not so many solvable discrete initial value problems related to this one, showing its specificity, which is a bit surprising result. Discrete initial value problem (dpeaa)DE-He213 Nonlinear difference equation (dpeaa)DE-He213 Closed-form formula (dpeaa)DE-He213 Solvable equation (dpeaa)DE-He213 Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2021(2021), 1 vom: 30. Jan. (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2021 year:2021 number:1 day:30 month:01 https://dx.doi.org/10.1186/s13662-021-03251-w kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE 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_74 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 31.49 ASE AR 2021 2021 1 30 01
allfieldsSound	10.1186/s13662-021-03251-w doi (DE-627)SPR042943671 (DE-599)SPRs13662-021-03251-w-e (SPR)s13662-021-03251-w-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Stević, Stevo verfasserin aut Note on a discrete initial value problem from a competition 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The following discrete initial value problem xn+1=xn(xn−12−2)−x1,n∈N,%$ x_{n+1}=x_{n}\bigl(x_{n-1}^{2}-2 \bigr)-x_{1},\quad n\in {\mathbb{N}}, %%$x_{0}=2$ and $x_{1}=5/2$, appeared at an international competition. It is known that the problem can be solved in closed form. Here we discuss the solvability of a more general initial value problem which includes the former one. We show that, in a sense, there are not so many solvable discrete initial value problems related to this one, showing its specificity, which is a bit surprising result. Discrete initial value problem (dpeaa)DE-He213 Nonlinear difference equation (dpeaa)DE-He213 Closed-form formula (dpeaa)DE-He213 Solvable equation (dpeaa)DE-He213 Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2021(2021), 1 vom: 30. Jan. (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2021 year:2021 number:1 day:30 month:01 https://dx.doi.org/10.1186/s13662-021-03251-w kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE 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_74 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 31.49 ASE AR 2021 2021 1 30 01
language	English
source	Enthalten in Advances in difference equations 2021(2021), 1 vom: 30. Jan. volume:2021 year:2021 number:1 day:30 month:01
sourceStr	Enthalten in Advances in difference equations 2021(2021), 1 vom: 30. Jan. volume:2021 year:2021 number:1 day:30 month:01
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Discrete initial value problem Nonlinear difference equation Closed-form formula Solvable equation
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container_title	Advances in difference equations
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author	Stević, Stevo
spellingShingle	Stević, Stevo ddc 510 bkl 31.49 misc Discrete initial value problem misc Nonlinear difference equation misc Closed-form formula misc Solvable equation Note on a discrete initial value problem from a competition
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topic_title	510 610 ASE 31.49 bkl Note on a discrete initial value problem from a competition Discrete initial value problem (dpeaa)DE-He213 Nonlinear difference equation (dpeaa)DE-He213 Closed-form formula (dpeaa)DE-He213 Solvable equation (dpeaa)DE-He213
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title_sort	note on a discrete initial value problem from a competition
title_auth	Note on a discrete initial value problem from a competition
abstract	Abstract The following discrete initial value problem xn+1=xn(xn−12−2)−x1,n∈N,%$ x_{n+1}=x_{n}\bigl(x_{n-1}^{2}-2 \bigr)-x_{1},\quad n\in {\mathbb{N}}, %%$x_{0}=2$ and $x_{1}=5/2$, appeared at an international competition. It is known that the problem can be solved in closed form. Here we discuss the solvability of a more general initial value problem which includes the former one. We show that, in a sense, there are not so many solvable discrete initial value problems related to this one, showing its specificity, which is a bit surprising result.
abstractGer	Abstract The following discrete initial value problem xn+1=xn(xn−12−2)−x1,n∈N,%$ x_{n+1}=x_{n}\bigl(x_{n-1}^{2}-2 \bigr)-x_{1},\quad n\in {\mathbb{N}}, %%$x_{0}=2$ and $x_{1}=5/2$, appeared at an international competition. It is known that the problem can be solved in closed form. Here we discuss the solvability of a more general initial value problem which includes the former one. We show that, in a sense, there are not so many solvable discrete initial value problems related to this one, showing its specificity, which is a bit surprising result.
abstract_unstemmed	Abstract The following discrete initial value problem xn+1=xn(xn−12−2)−x1,n∈N,%$ x_{n+1}=x_{n}\bigl(x_{n-1}^{2}-2 \bigr)-x_{1},\quad n\in {\mathbb{N}}, %%$x_{0}=2$ and $x_{1}=5/2$, appeared at an international competition. It is known that the problem can be solved in closed form. Here we discuss the solvability of a more general initial value problem which includes the former one. We show that, in a sense, there are not so many solvable discrete initial value problems related to this one, showing its specificity, which is a bit surprising result.
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title_short	Note on a discrete initial value problem from a competition
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