On Conditions of the Nonexistence of Solutions of Nonlinear Equations with Data from Classes Close to L1

A. A. Kovalevsky; F. Nicolosi

doi:10.4208/jpde.v26.n1.4

On Conditions of the Nonexistence of Solutions of Nonlinear Equations with Data from Classes Close to L1

Authors

A. A. Kovalevsky Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, R. Luxemburg St. 74, 83114 Donetsk, Ukraine
F. Nicolosi Department of Mathematics and Informatics, University of Catania, Viale A. Doria 6, 95125 Catania, Italy

DOI:

https://doi.org/10.4208/jpde.v26.n1.4

Keywords:

Nonlinear elliptic equations in divergence form;Dirichlet problem;weak solution;existence and nonexistence of weak solutions

Abstract

We establish conditions of the nonexistence of weak solutions of the Dirichlet problem for nonlinear elliptic equations of arbitrary even order with some righthand sides from L^m where m > 1. The conditions include the requirement of a certain closeness of the parameter m to 1.

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Published

2018-08-16

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Issue

Vol. 26 No. 1 (2013)

Section

Articles

How to Cite

On Conditions of the Nonexistence of Solutions of Nonlinear Equations with Data from Classes Close to L1. (2018). Journal of Partial Differential Equations, 26(1), 39-47. https://doi.org/10.4208/jpde.v26.n1.4