A Multiplicity Result for an Elliptic Anisotropic Differential Inclusion Involving Variable Exponents

作者：Costea Nicusor^*; Morosanu Gheorghe

来源：Set-Valued and Variational Analysis, 2013, 21(2): 311-332.

DOI：10.1007/s11228-012-0224-1

• Clarke's generalized gradient
• Differential inclusion
• Nonhomogeneous differential operator
• Anisotropic Sobolev spaces
• Nonsmooth critical point
• Multiple weak solutions

In this paper we are concerned with the study of a class of quasilinear elliptic differential inclusions involving the anisotropic -Laplace operator, on a bounded open subset of which has a smooth boundary. The abstract framework required to study this kind of differential inclusions lies at the interface of three important branches in analysis: nonsmooth analysis, the variable exponent Lebesgue-Sobolev spaces theory and the anisotropic Sobolev spaces theory. Using the concept of nonsmooth critical point we are able to prove that our problem admits at least two non-trivial weak solutions.

• 出版日期2013-6