Existence of solutions for a nonlinear system with a parameter

Abstract

In this paper, the existence of solutions for a system of nonlinear equations is considered. 2 n nonzero real solutions are obtained by using the critical point theory. Additionally, the Dirichlet boundary value problems of even order difference equations and partial difference equations are investigated.  2005 Elsevier Inc. All rights reserved.

An application of the Krasnoselskii theorem to systems of algebraic equations

“…There remains a great deal of algebraic problems, in particular, systems of algebraic equations, to be further investigated. A recent series of papers by Yang and Zhang [12], Zhang and Cheng [13], Zhang [14] and Zhang and Feng [15] studied the solutions of systems of nonlinear algebraic equations arising from systems of differential and difference equations and obtained a number of interesting results. In many nonlinear phenomena, only nonnegative solutions make sense and negative solutions may be translated into positive solutions.…”

“…In [12][13][14], the variational arguments are used to study the existence of solutions of the system of algebraic equations of the form…”

“…, n. Equation (2) can be converted into (1) by multiplying the inverse of B. Note that [14] corrects some errors in [13]. An analogous problem to the existence of positive solutions of (1) is the existence of positive solutions of systems of differential equations, which have been given considerable attention in the last few decades.…”

“…Not only do we extend the results in [15] in such a way that f (i) may depend on all x i (Example 2), but also all components of the left side of (1) are completely independent as A is allowed to be a nonnegative matrix in this paper. While the solutions of (2) studied in [12][13][14] are not necessarily positive, some negative solutions may be converted into nonnegative solutions such as in the case that…”

On some variational algebraic problems

“…For a survey on these topics we cite the recent paper [25]. A similar approach has also been used in others works (see for instance, the papers [21][22][23] and [24,26,27]). …”