Ayazoglu (Mashiyev), RabilAkbulut, SezginAkkoyunlu, Ebubekir2024-10-042024-10-0420200170-42141099-1476https://doi.org/10.1002/mma.6626http://hdl.handle.net/20.500.12403/3299In this paper, we prove the existence of multiple solutions for the nonhomogeneous Schrodinger-Kirchhoff-type problem involving the p(.)-Laplacian {-(1+b integral(N)(R)1/p(x)vertical bar del u vertical bar(p(x)) dx) Delta(p(x))u+V(x)vertical bar u vertical bar p((x)-2) u=f(x,u) + g(x) in R-N, u is an element of W-1,W-p(.)(R-N), where b >= 0 is a constant, N >= 2, Delta(p)(.)u := div(vertical bar del u vertical bar p((.)-2)del u) is the p(.)-Laplacian operator, p : R-N -> R is Lipschitz continuous, V : R-N -> R is a coercive type potential, integral : R-N x R -> R and g : R-N -> R functions verifying suitable conditions. We propose different assumptions on the nonlinear term f : R-N x R -> R to yield bounded Palais-Smale sequences and then prove that the special sequences we found converge to critical points, respectively. The solutions are obtained by the Mountain Pass Theorem, Ekeland variational principle, and Krasnoselskii genus theory.eninfo:eu-repo/semantics/closedAccessEkeland variational principleKrasnoselskii genus theoryLebesgue and Sobolev space with variable exponentMountain Pass Theoremp(.)-LaplacianSchrodinger-Kirchhoff-type equationArticle43179598961410.1002/mma.66262-s2.0-85088400859Q1WOS:000551337300001Q1