Superlinear (p(z), q(z))-equations

We consider Dirichlet boundary value problems for equations involving the (p(z), q(z))-Laplacian operator in the principal part and prove the existence of one and three nontrivial weak solutions, respectively. Here, the nonlinearity in the reaction term is allowed to depend on the solution, but does...

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Bibliographic Details
Published in:Complex variables and elliptic equations 2019-01, Vol.64 (1), p.8-25
Main Authors: Papageorgiou, N. S., Vetro, C.
Format: Article
Language:English
Subjects:
Boundary value problems
condition
critical groups
Dirichlet problem
Mathematical analysis
nonlinear regularity
Operators (mathematics)
p(z)
q(z))-Laplacian operator
weak solution
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Summary:We consider Dirichlet boundary value problems for equations involving the (p(z), q(z))-Laplacian operator in the principal part and prove the existence of one and three nontrivial weak solutions, respectively. Here, the nonlinearity in the reaction term is allowed to depend on the solution, but does not satisfy the Ambrosetti-Rabinowitz condition. The hypotheses on the reaction term ensure that the Euler-Lagrange functional, associated to the problem, satisfies both the -condition and a mountain pass geometry.
ISSN:1747-6933
1747-6941
DOI:10.1080/17476933.2017.1409743