Variable exponent \(p(\cdot)\)-Kirchhoff type problem with convection in variable exponent Sobolev spaces. (English) Zbl 07805688
Summary: We establish the existence of weak solution for a class of \(p(x)\)-Kirchhoff type problem for the \(p(x)\)-Laplacian-like operator with Dirichlet boundary condition and with gradient dependence (convection) in the reaction term. Our result is obtained using the topological degree for a class of demicontinuous operators of generalized \((S_+)\) type and the theory of the variable exponent Sobolev spaces. Our results extend and generalize several corresponding results from the existing literature.
MSC:
| 35J93 | Quasilinear elliptic equations with mean curvature operator |
| 35J66 | Nonlinear boundary value problems for nonlinear elliptic equations |
| 35D30 | Weak solutions to PDEs |
| 47H11 | Degree theory for nonlinear operators |
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