On a class of \(p(x, \cdot )\)-integro-differential Kirchhoff-type problem with singular kernel. (English) Zbl 07925052
Summary: In this paper, we consider a class of \(p(x, \cdot )\)-integro-differential Kirchhoff-type problem with Dirichlet boundary conditions. Considering various variational methods, we establish the existence of multiple solutions taking into account the different situations concerning the non-linearity and growth conditions.
MSC:
| 35R11 | Fractional partial differential equations |
| 45K05 | Integro-partial differential equations |
| 47G20 | Integro-differential operators |
| 45H05 | Integral equations with miscellaneous special kernels |
| 35S05 | Pseudodifferential operators as generalizations of partial differential operators |
| 35A15 | Variational methods applied to PDEs |
Keywords:
general nonlocal integro-differential equation; variational methods; \(p(x, \cdot )\)-Kirchhoff type problem; generalized fractional Sobolev spacesReferences:
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