Electron. J. Differential Equations, Vol. 2016 (2016), No. 313, pp. 1-9.

Nontrivial solutions for nonlinear algebraic systems via a local minimum theorem for functionals

Ghasem A. Afrouzi, Armin Hadjian

In this article, we use a critical point theorem (local minimum result) for differentiable functionals to prove the existence of at least one nontrivial solution for a nonlinear algebraic system with a parameter. Our goal is achieved by requiring an appropriate asymptotic behavior of the nonlinear term at zero. Some applications to discrete equations are also presented.

Submitted April 23, 2016. Published December 10, 2016.
Math Subject Classifications: 39A10, 34B15.
Key Words: Discrete nonlinear boundary value problems; existence; difference equations; critical points theory.

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Ghasem A. Afrouzi
Department of Mathematics
Faculty of Mathematical Sciences
University of Mazandaran
Babolsar, Iran
email: afrouzi@umz.ac.ir
Armin Hadjian
Department of Mathematics
Faculty of Basic Sciences
University of Bojnord
P.O. Box 1339, Bojnord 94531, Iran
email: hadjian83@gmail.com, a.hadjian@@ub.ac.ir

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