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Indefinite Quasilinear Neumann Problem on Unbounded Domains

J. Chabrowski (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

We investigate the solvability of the quasilinear Neumann problem (1.1) with sub- and supercritical exponents in an unbounded domain Ω. Under some integrability conditions on the coefficients we establish embedding theorems of weighted Sobolev spaces into weighted Lebesgue spaces. This is used to obtain solutions through a global minimization of a variational functional.

Infinite multiplicity of positive solutions for singular nonlinear elliptic equations with convection term and related supercritical problems.

Aranda, Carlos C. (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Infinitely many periodic solutions for variable exponent systems.

Guo, Xiaoli, Lu, Mingxin, Zhang, Qihu (2009)

Journal of Inequalities and Applications [electronic only]

Integrability for solutions to quasilinear elliptic systems

Francesco Leonetti, Pier Vincenzo Petricca (2010)

Commentationes Mathematicae Universitatis Carolinae

In this paper we prove an estimate for the measure of superlevel sets of weak solutions to quasilinear elliptic systems in divergence form. In some special cases, such an estimate allows us to improve on the integrability of the solution.

Inverse eigenvalue problems for semilinear elliptic equations.

Shibata, Tetsutaro (2009)