The existence and multiplicity of positive solutions for quasilinear elliptic equations with nonhomogeneous principal part are discussed. The lower terms considered here have the Sobolev critical growth and have indefinite coefficients. We show that the strong comparison theorem holds for these equations. By this fact and regularity theorem, "C1 versus Sobolev space local minimizers" argument may be applied, which yields a local minimizer of the functional attached to the equation defined on the Sobolev space. Finally applying the minimax theorem and the concentration-compactness argument, we show the multiple existence of positive solutions.
Multiple existence of positive solutions to quasilinear elliptic equations involving indefinite lower terms
9TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2012 ; 2012 ; Vienna, Austria
AIP Conference Proceedings ; 1493 , 1 ; 691-698
2012-11-06
8 pages
Conference paper
Electronic Resource
English
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