# On the existence of solutions of some second order nonlinear difference equations

Małgorzata Migda; Ewa Schmeidel; Małgorzata Zbąszyniak

Archivum Mathematicum (2005)

- Volume: 041, Issue: 4, page 379-388
- ISSN: 0044-8753

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topMigda, Małgorzata, Schmeidel, Ewa, and Zbąszyniak, Małgorzata. "On the existence of solutions of some second order nonlinear difference equations." Archivum Mathematicum 041.4 (2005): 379-388. <http://eudml.org/doc/249499>.

@article{Migda2005,

abstract = {We consider a second order nonlinear difference equation \[ \Delta ^2 y\_n = a\_n y\_\{n+1\} + f(n,y\_n,y\_\{n+1\})\,,\quad n\in N\,. \qquad \mathrm \{(\mbox\{E\})\}\]
The necessary conditions under which there exists a solution of equation (E) which can be written in the form \[ y\_\{n+1\} = \alpha \_\{n\}\{u\_n\} + \beta \_\{n\}\{v\_n\}\,,\quad \mbox\{are given.\} \]
Here $u$ and $v$ are two linearly independent solutions of equation \[ \Delta ^2 y\_n = a\_\{n+1\} y\_\{n+1\}\,, \quad (\{\lim \limits \_\{n \rightarrow \infty \} \alpha \_\{n\} = \alpha <\infty \} \quad \{\rm and\} \quad \{\lim \limits \_\{n \rightarrow \infty \} \beta \_\{n\} = \beta <\infty \})\,. \]
A special case of equation (E) is also considered.},

author = {Migda, Małgorzata, Schmeidel, Ewa, Zbąszyniak, Małgorzata},

journal = {Archivum Mathematicum},

keywords = {nonlinear difference equation; nonoscillatory solution; second order; nonoscillatory solution},

language = {eng},

number = {4},

pages = {379-388},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {On the existence of solutions of some second order nonlinear difference equations},

url = {http://eudml.org/doc/249499},

volume = {041},

year = {2005},

}

TY - JOUR

AU - Migda, Małgorzata

AU - Schmeidel, Ewa

AU - Zbąszyniak, Małgorzata

TI - On the existence of solutions of some second order nonlinear difference equations

JO - Archivum Mathematicum

PY - 2005

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 041

IS - 4

SP - 379

EP - 388

AB - We consider a second order nonlinear difference equation \[ \Delta ^2 y_n = a_n y_{n+1} + f(n,y_n,y_{n+1})\,,\quad n\in N\,. \qquad \mathrm {(\mbox{E})}\]
The necessary conditions under which there exists a solution of equation (E) which can be written in the form \[ y_{n+1} = \alpha _{n}{u_n} + \beta _{n}{v_n}\,,\quad \mbox{are given.} \]
Here $u$ and $v$ are two linearly independent solutions of equation \[ \Delta ^2 y_n = a_{n+1} y_{n+1}\,, \quad ({\lim \limits _{n \rightarrow \infty } \alpha _{n} = \alpha <\infty } \quad {\rm and} \quad {\lim \limits _{n \rightarrow \infty } \beta _{n} = \beta <\infty })\,. \]
A special case of equation (E) is also considered.

LA - eng

KW - nonlinear difference equation; nonoscillatory solution; second order; nonoscillatory solution

UR - http://eudml.org/doc/249499

ER -

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