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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.

electronic journal on the qualitative theory of differential equations

Existence results for a nonlinear elliptic transmission problem of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mrow> <mml:mo form="prefix">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo form="postfix">)</mml:mo> </mml:mrow> </mml:mrow> </mml:math>-Kirchhoff type

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