Abstract
This paper deals with the following Kirchhoff type problem (0.1)−a+b∫RN|∇u|2Δu=λK(x)uq−1+u2∗−1,u>0,x∈RN,where N≥3, K∈L1(RN)∩L∞(RN), constants a,b>0, the parameter λ>0 and 2≤q<2∗≔2N∕(N−2). Using the finite-dimensional reduction approach, we prove that problem (0.1) admits at least a positive solution.
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