On a nonhomogeneous Kirchhoff-type elliptic problem with critical exponential in dimension two

In this article, the Ekeland variational principle, mountain pass theorem and Trudinger-Moser inequality are applied to establish the existence and multiplicity of solutions for the following nonhomogeneous Kirchhoff-type elliptic problem: -m(integral(Omega)vertical bar del u vertical bar(2) dx) Delta u = f (x, u) + epsilon h(x) in Omega; u = 0 on partial derivative Omega, where Omega is a smooth bounded domain in R-2, m : R+ -> R+ is a Kirchhoff function, f : Omega x R. R is a continuous function, h epsilon (W-0(1,2) (Omega)) * = W--1,W-2, h = 0, h not equivalent to 0, and epsilon is a small positive parameter. The nonlinearity term f (x, s) behaves like e(alpha 0s2) when vertical bar s vertical bar -> infinity for some alpha(0) > 0.

Automated summary

In this article, the Ekeland variational principle, mountain pass theorem, and Trudinger-Moser inequality are used to establish the existence and multiplicity of solutions for a nonhomogeneous Kirchhoff-type elliptic problem.