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Existence and multiplicity results for nonlinear problems involving the p(x)-laplace operator

Tsouli N., Darhouche O.

Opuscula Mathematica

2014

Vol. 34, no. 3

621--638

In this paper we study the following nonlinear boundary-value problem [formula] where Ω ⊂ RN is a bounded domain with smooth boundary [formula] is the outer unit normal derivative on [formula] are two real numbers such that [formula] is a continuous function on Ω with [formula] are continuous functions. Under appropriate assumptions on ƒ and g, we obtain the existence and multiplicity of solutions using the variational method. The positive solution of the problem is also considered.