## Existence of a positive solution for a Kirchhoff problem type with critical growth via truncation argument.(English)Zbl 1307.35110

Summary: We shall show an existence result of a positive solution for a Kirchhoff problem type in a bounded domain of $$\mathbb R^N$$, that is, for the problem $-M\left(\int_\Omega|\nabla u|^2dx\right)\Delta u=\lambda f(x,u)+|u|^{2^*-2}u\;\text{in}\;\Omega,\;u=0\;\text{on}\;\partial\Omega.$ We shall study the asymptotic behavior of this solution when $$\lambda$$ converges to infinity. Our approach is based on the variational method, an appropriated truncated argument, and a priori estimates to obtain the solution.

### MSC:

 35J60 Nonlinear elliptic equations 35J20 Variational methods for second-order elliptic equations
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