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Nontrivial solution for a nonlocal elliptic transmission problem in variable exponent Sobolev spaces. (English) Zbl 1216.35162

Summary: By means of adequate variational techniques and the theory of the variable exponent Sobolev spaces, we show the existence of nontrivial solution for a transmission problem given by a system of two nonlinear elliptic equations of \(p(x)\)-Kirchhoff type with nonstandard growth condition.

MSC:

35R09 Integro-partial differential equations
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
47J05 Equations involving nonlinear operators (general)
47J30 Variational methods involving nonlinear operators
35A15 Variational methods applied to PDEs
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