Existence of Solutions for a Class of Elliptic Systems in Involving the -Laplacian

Existence Results for A Nonlocal Problem Involving the p(x)-Laplacian

“…This causes many problems, some classical theories and methods, such as the Lagrange multiplier theorem and the theory of Sobolev spaces, are not applicable. For p(x)-Laplacian operator, we refer the readers to [9,10,17,18] and references there in. Moreover, the nonlinear problems involving the p(x)-Laplacian operator are extremely attractive because they can be used to model dynamical phenomenons which arise from the study of electrorheological fluids or elastic mechanics.…”

Existence of solutions for a class of strongly coupled $p(x)-$ laplacian system

“…Introducing some natural growth hypotheses on the right-hand side of the system which will ensure the semi-continuous and coercivity for the corresponding Euler-Lagrange functional of the system, the authors use critical point theory to obtain the existence of nontrivial weak solution of the system (1.3). In Ogras-Mashiyev-Avci-Yucedag [13] using a weak version of the Palais-Smale condition, that is, Cerami condition, they apply the mountain pass theorem to get the nontrivial solutions of the system (1.3).…”

Existence of Solutions for Critical Systems With Variable Exponents

“…Such problems have attracted an increasing attention and many results have been obtained by several authors. We would mention to ( [3], [4], [16], [19], [20], [26], [30], [31]) and survey papers ( [8], [10], [14], [21], [24], [27], [29]) for the advances and references in this area.…”