The object of this paper is to study a nonlocal problem involving the p(x)-Laplacian where nonlinearities f do not necessarily satisfy the classical conditions, such as Ambrosetti-Rabinowitz condition, but are limited by functions that do satisfy some specific conditions. By using the direct variational approach and the theory of the variable exponent Sobolev spaces, the existence and uniqueness of solutions is obtained.
|Number of pages
|Annals of the University of Craiova, Mathematics and Computer Science Series
|Published - 2014
- Nonlocal problems
- Variable exponent sobolev spaces
- Variational method