Existence results for a nonlinear elliptic transmission problem of $p(x)$-Kirchhoff type

• Main Authors: Eugenio Cabanillas Lapa, Felix Leon Barboza, Juan Benito Bernui Barros, Benigno Godoy Torres
• Format: Article
• Language: English
• Published: University of Szeged 2016-11-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: nonlinear transmission problem; p(x)-laplacian; monotone operator
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=4945
• ISSN: 1417-3875; 1417-3875

In this article, we establish the existence of weak solutions for a nonlinear transmission problem involving nonlocal coefficients of $p(x)$-Kirchhoff type in two different domains, which are connected by a nonlinear transmission condition at their interface. We get our results by means of the monotone operator theory and the $(S_{+})$ mapping theory; the weak formulation takes place in suitable variable exponent Sobolev spaces.