Resumen de Existence and Asymptotic Behavior of Solutions for Kirchhoff Type Equations with Critical Exponent and a Logarithmic Term
Anran Li, Chongqing Wei, Xiaozhen Zhang
In this paper, a class of Kirchhoff equations on a bounded domain with a combination of critical and logarithmic terms is studied by variational methods. Firstly, a mountain pass solution to the equation is obtained by using Lions’ second concentration compactness principle and an estimate of the logarithmic term, which is also the ground state solution of it. Secondly, the multiplicity of solutions to the equation is got by a version of symmetry mountain pass theorem. Finally, the asymptotic behavior of the solutions as the coefficient of the nonlocal term tends to zero is studied.
