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

Avci M.

Opuscula Mathematica

2018

Vol. 38, no. 3

291--305

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.

Landau-type theorem for variable Lebesgue spaces

Maligranda L., Wnuk W.

Commentationes Mathematicae

2015

Vol 55, No. 2

119--126

We describe, using elementary methods, the Köthe dual of variable Lebesgue spaces Lp(⋅), called also Nakano spaces, independenly for p(⋅)∈(1,∞) and p(⋅)∈(0,1). The case when p(⋅)∈[1,∞] is also included.