Existence of positive solutions for nonlinear Kirchhoff type problems in R3 with critical Sobolev exponent

By Gongbao Li, Hongyu Ye. 2013

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In this paper, we study the following nonlinear problem of Kirchhoff type with critical Sobolev exponent: −a+b∫R3|Du|2Δu+u=f(x,u)+u5,x∈R3,u∈H1(R3),u>0,x∈R3, where a, b > 0 are constants. Under certain assumptions on the sign‐changing function f(x,u), we prove the existence of positive solutions by variational methods.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

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