Abstract
Abstract We consider a nonlinear parametric Dirichlet problem driven by the (p, q)-Laplacian (double phase problem) with a reaction exhibiting the competing effects of three different terms. A parametric one consisting of the sum of a singular term and of a drift term (convection) and of a nonparametric perturbation which is resonant. Using the frozen variable method and eventually a fixed point argument based on an iterative asymptotic process, we show that the problem has a positive smooth solution.
Highlights
Let Ω ⊆ RN be a bounded domain with a C -boundary ∂Ω
We consider a nonlinear parametric Dirichlet problem driven by the (p,q)-Laplacian with a reaction exhibiting the competing e ects of three di erent terms
A parametric one consisting of the sum of a singular term and of a drift term and of a nonparametric perturbation which is resonant
Summary
In this paper we study the following parametric singular double phase Dirichlet problem with gradient dependence (convection). In problem (Eλ) we have the sum of two such operators with di erent exponents. The di erential operator of the problem is not homogeneous. In the reaction (right hand side of (Eλ)), we have the combined e ects of three terms, each of di erent nature. There is a parametric contribution which is the sum of a singular term and of a gradient dependent term (a drift term). Both are multiplied with the parameter λ >. The presence of the drift term makes the problem nonvariational and so our method of proof will be topological.
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