Existence result for a double phase problem involving the \((p(x),q(x))\)-Laplacian operator. (English) Zbl 1522.35282
Summary: The Dirichlet boundary value problem for elliptic equations involving the \((p(x), q(x))\)-Laplacian operator with a reaction term depending on the gradient and on two real parameters is considered in this paper. Using the topological degree theory for a class of demicontinuous operators of generalized \((S_+)\) and the theory of the variable exponent Sobolev spaces, we prove the existence of at least one weak solution of such problem.
MSC:
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 47H11 | Degree theory for nonlinear operators |
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