Liouville theorems for elliptic inequalities and applications
- 1 January 1998
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 128 (6) , 1217-1247
- https://doi.org/10.1017/s0308210500027293
Abstract
In this paper we prove nonexistence of positive C2 solutions for systems of semilinear elliptic inequalities, for polyharmonic semilinear inequalities in cones and, under better conditions on the nonlinearity, for bounded positive solutions of elliptic semilinear equations in half spaces. Using a blow-up argument, these results allow us to prove a-priori bounds for a class of semilinear elliptic systems of equations in bounded domains.Keywords
This publication has 12 references indexed in Scilit:
- Elliptic Partial Differential Equations of Second OrderPublished by Springer Nature ,2001
- Nonexistence of positive solutions of quasilinear equationsAdvances in Differential Equations, 1997
- A priori estimates and existence of positive solutions of nonlinear cooperative elliptic systemsDifferential and Integral Equations, 1995
- Superlinear indefinite elliptic problems and nonlinear Liouville theoremsTopological Methods in Nonlinear Analysis, 1994
- The principal eigenvalue and maximum principle for second‐order elliptic operators in general domainsCommunications on Pure and Applied Mathematics, 1994
- Department of technical mathematics and informatics university of technologyCommunications in Partial Differential Equations, 1993
- Some notes on the method of moving planesBulletin of the Australian Mathematical Society, 1992
- Global and local behavior of positive solutions of nonlinear elliptic equationsCommunications on Pure and Applied Mathematics, 1981
- A priori bounds for positive solutions of nonlinear elliptic equationsCommunications in Partial Differential Equations, 1981
- Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. ICommunications on Pure and Applied Mathematics, 1959