The Existence Of Positive Solution For The Kirchhoff Equation With A General Nonlinearity Involving Critical Growth

In this thesis, we consider the following nonlinear Kirchhoff problem involving critical growth with general nonlinearities: where a, b> 0 are constants. Under some suitable assumptions on the potential V(x), the weight function Q(x) and f(u), we prove that there exists a positive ground state solution for the problem (). We mention here that we do not assume f(u) verifies the Ambrosetti-Rabinowitz condition and f(u) may not be homogeneous with respect to u.Our main results can be seen as an extension for the paper [Calc.Var.PDE.,54 (2015) 3067-3106] by Y.He and G.Li dealing with the existence of positive solution for the following Kirchhoff problem where ∈, λ> 0 are paremeters, V(x) is a positive and continuous potential.