Existence results for a Neumann problem involving thep(x)-Laplacian with discontinuous nonlinearities

On a p ( x ) $p(x)$ -biharmonic problem with Navier boundary condition

“…In recent years, the study on variational problems with variable exponent is an interesting topic, which arises from nonlinear electrorheological fluids and elastic mechanics (see [1][2][3]). We also refer to [4][5][6][7][8][9][10][11][12][13][14] for an overview.…”

Infinitely many solutions for equations of p(x)-Laplace type with the nonlinear Neumann boundary condition

“…To the best of our knowledge, most of the results about the existence of weak solutions for Neumann problems are derived under the AR condition; see [6,8,28,38,40,41]. Inspired by the papers [3,18,22,26,30], we demonstrate our result in a more general setting.…”

“…Following the basic ideas of [26], Chung and Toan [9] considered a class of nonlinear and non-homogeneous problems in an Orlicz-Sobolev space setting. Recently, using an abstract result contained in [5], the authors in [2,3] obtained the existence of a non-trivial weak solution for a parametric Neumann problem driven by the p(x)-Laplacian without the AR condition.…”

Multiple Solutions for a Class of (P1(x), P2(x))-Laplacian Problems With Neumann Boundary Conditions

“…Let X 0 be a bounded subset of X. By (5) and (6), and the continuous embeddings N. Thanh Chung -Multiple solutions for a class of (p…”

“…For more information on modeling physical phenomena by equations involving p(x)-growth condition we refer to [1]. p(x)-Laplacian problems have intensively studied in many papers, we refer to some interesting papers [5,8,11,19,22] in which the nonlinear terms f (x, t) and g(x, t) are subcritical and sublinear (or superlinear) at infinity with respect to the second variable t ∈ R.…”