Opuscula Math. 38, no. 3 (2018), 291-305
https://doi.org/10.7494/OpMath.2018.38.3.291

Opuscula Mathematica

# Solutions to p(x)-Laplace type equations via nonvariational techniques

Mustafa Avci

Abstract. In this article, we consider a class of nonlinear Dirichlet problems driven by a Leray-Lions type operator with variable exponent. The main result establishes an existence property by means of nonvariational arguments, that is, nonlinear monotone operator theory and approximation method. Under some natural conditions, we show that a weak limit of approximate solutions is a solution of the given quasilinear elliptic partial differential equation involving variable exponent.

Keywords: Leray-Lions type operator, nonlinear monotone operator, approximation, variable Lebesgue spaces.

Mathematics Subject Classification: 35J60, 35J70, 35J92, 58E05, 76A02.

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• Mustafa Avci
• Faculty of Economics and Administrative Sciences, Batman University, Turkey
• Communicated by Vicentiu D. Radulescu.
• Revised: 2017-12-22.
• Accepted: 2018-01-07.
• Published online: 2018-03-19.