Abstract

In this article, we establish the existence of at least one non-trivial classical solution for a class of elliptic equations involving a general operator in divergence form, subject to Dirichlet boundary conditions in a smooth bounded domain in $\mathbb{R}^N$. A critical point result for differentiable functionals is discussed. Our technical approach is based on variational methods. In addition, an example to illustrate our results is given.

Keywords: Existence result; weak solution; divergence type equations; variational methods; critical point theory.

MSC: 35J35, 35J60

DOI: 10.57016/MV-KG8494SM

Pages:  157$-$165     

Volume  75 ,  Issue  3 ,  2023