Shapour Heidarkhani, Anderson L. A. De Araujo, Giuseppe Caristi, and Amjad Salari. Multiplicity results for nonlocal problems with variable exponent and nonhomogeneous Neumann conditions. Dynamic Systems and Applications 30 (2021) No. 7, 1149-1179

https://doi.org/10.46719/dsa20213076

ABSTRACT.
This article is concerned with the multiplicity results for nonlocal problems with
variable exponent and nonhomogeneous Neumann conditions. In fact, using variational methods and
critical point theory we look into the existence results for the problem under algebraic conditions
with the classical Ambrosetti-Rabinowitz (AR) condition on the nonlinear term. Furthermore, by
combining two algebraic conditions on the nonlinear term which guarantees the existence of two
solutions, applying the mountain pass theorem given by Pucci and Serrin we establish the existence
of a third solution for our problem.

AMS (MOS) Subject Classication. 35J20, 35J60.
Key Words and Phrases. Multiple solutions; Variable exponent Sobolev spaces; p(x)-Laplacian;
Nonhomogeneous Neumann condition; Variational methods; Critical point theory.