Abstract
Three solutions for second-order boundary-value problems with variable exponents
Highlights
The study of various problems with the variable exponent has received considerable attention in recent years both for their interesting in applications and for the many mathematical questions arising from such problems
The necessary framework for the study of these problems is represented by the function spaces with variable exponent Lp(x)(Ω) and Wm,p(x)(Ω)
Bonanno and Chinnì in [3] by using a multiple critical points theorem for non-differentiable functionals, investigated the existence and multiplicity of solutions for the following problem
Summary
The aim of this paper is to consider the following boundary value problem involving an ordinary differential equation with p(x)-Laplacian operator and nonhomogeneous Neumann conditions. Bonanno and Chinnì in [3] by using a multiple critical points theorem for non-differentiable functionals, investigated the existence and multiplicity of solutions for the following problem. Cammaroto et al in [8] by using a three critical points theorem due to Ricceri, obtained the existence of three weak solutions for the following problem. Motivated by the above facts, in the present paper, by using a three critical point theorem which is a smooth version of [2, Theorem 3.3] (see [2, Remarks 3.9 and 3.10]) due Bonanno and Candito we study the existence of at least three non-trivial weak solution for the problem (Pλf,μ). A special case of our main result, Theorem 3.1, is the following theorem.
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