6533b824fe1ef96bd127ffdb
RESEARCH PRODUCT
The Existence of Solutions for Local Dirichlet (r(u),s(u))-Problems
Calogero Vetrosubject
General Mathematicsregularized problem(<i>r</i>(<i>u</i>)<i>s</i>(u))-Laplacian operatorPalais-Smale conditionweak solutionComputer Science::Digital Libraries(<i>r</i>(<i>u</i>)<i>s</i>(u))-Laplacian operator; Palais-Smale condition; monotone operator; regularized problem; weak solutionSettore MAT/05 - Analisi Matematicamonotone operatorComputer Science (miscellaneous)QA1-939Computer Science::Programming Languages(r(u) s(u))-Laplacian operatorEngineering (miscellaneous)Mathematicsdescription
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 conditions to establish the existence of the solution to a regularized problem via variational methods and the critical point theory; and (ii) Sobolev nonlinearity, somehow related to the space structure. In this case, we use a priori estimates and asymptotic analysis of regularized auxiliary problems to establish the existence and uniqueness theorems via a fixed-point argument.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2022-01-13 | Mathematics |