%N 12
%K Laplace-egyenlet, Sobolev tĂŠr
%D 2023
%O Bibliogr.: p. 20-22. ; ĂśsszefoglalĂĄs angol nyelven
%C Szeged
%L acta82262
%X In this paper, we consider a mixed boundary value problem for nonuniformly elliptic equation in a variable exponent Sobolev space containing p(¡)-Laplacian and mean curvature operator. More precisely, we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show the existence of a nontrivial weak solution and at least two nontrivial weak solutions according to some hypotheses on given functions.
%A  Aramaki Junichi
%T Existence of nontrivial weak solutions for nonuniformly elliptic equation with mixed boundary condition in a variable exponent Sobolev space