We are concerned with the study of the existence and multiplicity of solutions for Dirichlet boundary value problems, involving the (p(m), q(m))− equation and the nonlinearity is superlinear but does not fulfil the Ambrossetti-Rabinowitz condition in the framework of Sobolev spaces with variable exponents in a complete manifold. The main results are proved using the mountain pass theorem and Fountain theorem with Cerami sequences. Moreover, an example of a (p(m), q(m)) equation that highlights the applicability of our theoretical results is also provided.
WEAK SOLVABILITY OF NONLINEAR ELLIPTIC EQUATIONS INVOLVING VARIABLE EXPONENTS
Ragusa M. A.
2023-01-01
Abstract
We are concerned with the study of the existence and multiplicity of solutions for Dirichlet boundary value problems, involving the (p(m), q(m))− equation and the nonlinearity is superlinear but does not fulfil the Ambrossetti-Rabinowitz condition in the framework of Sobolev spaces with variable exponents in a complete manifold. The main results are proved using the mountain pass theorem and Fountain theorem with Cerami sequences. Moreover, an example of a (p(m), q(m)) equation that highlights the applicability of our theoretical results is also provided.File in questo prodotto:
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