Positive solutions for nonparametric anisotropic singular solutions
Copyright policy )Positive solutions for nonparametric anisotropic singular solutions
We consider an elliptic equation driven by a nonlinear, nonhomogeneous differential operator with nonstandard growth. The reaction has the combined effects of a singular term and of a "superlinear" perturbation. There is no parameter in the problem. Using variational tools and truncation and comparison techniques, we show the existence of at least two positive smooth solutions.
T57-57.97, Applied mathematics. Quantitative methods, Positive solutions to PDEs, Comparison principles in context of PDEs, variable lebesgue and sobolev spaces, truncations and comparisons, anisotropic regularity, Maximum principles in context of PDEs, hardy inequality, Quasilinear elliptic equations, Variational and other types of inequalities involving nonlinear operators (general), Hardy inequality, variable Lebesgue and Sobolev spaces, anisotropic maximum principle, Singular elliptic equations, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Quasilinear elliptic equations with \(p\)-Laplacian
T57-57.97, Applied mathematics. Quantitative methods, Positive solutions to PDEs, Comparison principles in context of PDEs, variable lebesgue and sobolev spaces, truncations and comparisons, anisotropic regularity, Maximum principles in context of PDEs, hardy inequality, Quasilinear elliptic equations, Variational and other types of inequalities involving nonlinear operators (general), Hardy inequality, variable Lebesgue and Sobolev spaces, anisotropic maximum principle, Singular elliptic equations, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Quasilinear elliptic equations with \(p\)-Laplacian
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