Existence and bifurcation for some elliptic problems on exterior strip domains.
This paper discusses the existence and multiplicity of solutions for a class of -Kirchhoff type problems with Dirichlet boundary data of the following form where is a smooth open subset of and with , , are positive constants and is a continuous function. The proof is based on critical point theory and variable exponent Sobolev space theory.
We revisit Kristály’s result on the existence of weak solutions of the Schrödinger equation of the form -Δu + a(x)u = λb(x)f(u), , , where λ is a positive parameter, a and b are positive functions, while is sublinear at infinity and superlinear at the origin. In particular, by using Ricceri’s recent three critical points theorem, we show that, under the same hypotheses, a much more precise conclusion can be obtained.