Existence of solutions for a class of \(p(x)\)-Kirchhoff type equation with dependence on the gradient. (English) Zbl 1422.35048

Cabanillas Lapa, Eugeniox; Barros, Juan Benito Bernui; de la Cruz Marcacuzco, Rocio Julieta; Segura, Zacarias Huaringa

Kyungpook Math. J. 58, No. 3, 533-546 (2018).

Summary: The object of this work is to study the existence of solutions for a class of \(p(x)\)-Kirchhoff type problem under no-flux boundary conditions with dependence on the gradient. We establish our results by using the degree theory for operators of \((S_+)\) type in the framework of variable exponent Sobolev spaces.

MSC:

35J60	Nonlinear elliptic equations
35J92	Quasilinear elliptic equations with \(p\)-Laplacian
35A01	Existence problems for PDEs: global existence, local existence, non-existence

Keywords:

\(p(x)\)-Kirchhoff-type equation; variable exponent Sobolev space; degree theory

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