Article ID Journal Published Year Pages File Type
4589519 Journal of Functional Analysis 2017 54 Pages PDF
Abstract

We give necessary and sufficient conditions for the existence of weak solutions to the model equation−Δpu=σuqonRn, in the case 00b>0. These results are new even in the classical case p=2p=2.Our approach is based on the use of special nonlinear potentials of Wolff type adapted for “sublinear” problems, and related integral inequalities. It allows us to treat simultaneously several problems of this type, such as equations with general quasilinear operators divA(x,∇u), fractional Laplacians (−Δ)α(−Δ)α, or fully nonlinear k-Hessian operators.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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