2022
DOI: 10.3390/math10020237
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The Existence of Solutions for Local Dirichlet (r(u),s(u))-Problems

Abstract: In this paper, we consider local Dirichlet problems driven by the (r(u),s(u))-Laplacian operator in the principal part. We prove the existence of nontrivial weak solutions in the case where the variable exponents r,s are real continuous functions and we have dependence on the solution u. The main contributions of this article are obtained in respect of: (i) Carathéodory nonlinearity satisfying standard regularity and polynomial growth assumptions, where in this case, we use geometrical and compactness conditio… Show more

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Cited by 5 publications
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