open access

https://hdl.handle.net/2115/86438

Existence of minimal solutions to quasilinear elliptic equations with several sub-natural growth terms

英語

Wolff potential

2020-08

Elsevier

Nonlinear analysis. Theory, methods and applications

197

111847

We study the existence of positive solutions to quasilinear elliptic equations of the type -Delta(p)u = sigma u(q) + mu in R-n, in the sub-natural growth case 0 < q < p - 1, where Delta(p)u = del center dot (vertical bar del u vertical bar(p-2)del u) is the p-Laplacian with 1 < p < n, and sigma and mu are nonnegative Radon measures on R-n. We construct minimal generalized solutions under certain generalized energy conditions on sigma and mu. To prove this, we give new estimates for interaction between measures. We also construct solutions to equations with several sub-natural growth terms using the same methods. (C) 2020 Elsevier Ltd. All rights reserved.

学術雑誌論文

Accepted Manuscript

Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International

©2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

0362-546X