On Steklov–Neumann boundary value problems for some quasilinear elliptic equations

Abstract

a b s t r a c tIn this study, we consider a class of Steklov-Neumann boundary value problems for some quasilinear elliptic equations. We obtain result that ensure the existence of solutions when resonance and nonresonance conditions occur. The results are obtained using variational arguments.

ON STEKLOV BOUNDARY VALUE PROBLEMS FOR p(x)-LAPLACIAN EQUATIONS Vol. 5(2) July 2017, No. 28, pp. 289-297 I. EKINCIOGLU, R. AYAZOGLU(MASHIYEV)

“…In 2015 Godoi, Miyagaki, Rodrigues [14] provided existence results for the following class of Steklov-Neumann boundary value problems for some quasilinear elliptic equations…”

“…Be noted, …rstly in article [18], problem (P ) was addressed in condition p = 2. After, authors in article [14] generalized problem (P ) to p-Laplacian.…”

“…In [14] and [18], authors used inequalities kuk are norms in L p ( ) and L p (@ ), respectively. We note that we deal with the problem (P ) consist of p(x)-Laplacian, naturally, the solution of the problem have been made in the variable exponent Lebesgue-Sobolev spaces.…”

“…We note that we deal with the problem (P ) consist of p(x)-Laplacian, naturally, the solution of the problem have been made in the variable exponent Lebesgue-Sobolev spaces. Therefore, there exist constants 1 and 1 (see [14]). Thus, in this paper, we will discuss the inequalities…”