We investigate the eigenvalue problem for Kirchhoff type equations involving a superlinear perturbation, namely, −a∫RN|∇u|2dx+1Δu+μV(x)u=λf(x)u+g(x)|u|p−2u in RN, where V∈C(RN) is potential well with bottom Ω≔int{x∈RN|V(x)=0}. When N = 3 and 4 < p 6, each > 0 μ sufficiently large, we obtain at least one positive solution λ ≤ λ1(fΩ), while two solutions exist λ1(fΩ) + δa without an...

In this work, we consider the blow up of solutions for viscoelastic wave equation Kirchhoff type with variable exponents. The present result in work improve previous literature.