On existence and concentration of positive bound states of p-Laplacian equations in image involving critical growth Original Research Article

This paper deals with the study of the quasilinear critical problem equation(PεPε Turn MathJax on ) View the MathML source-εpΔpu+V(z)up-1=f(u)+up*-1inRN,u∈Cloc1,α(RN)∩W1,p(RN),u>0inRN, Turn MathJax on where εε is a small positive parameter; f is a subcritical nonlinearity; p*=pN/(N-p)p*=pN/(N-p), 1infΩV for some open bounded subset ΩΩ of RNRN. We study whether we can find solutions of (Pε)(Pε) which concentrate around a local minima of VV, not necessarily nondegenerate. The proof of this result is variational based on the local mountain-pass theorem.