Nonlinear Liouville theorems and a priori estimates for indefinite superlinear elliptic equations

By Yihong Du, Shujie Li. Advances in Differential Equations, 2005

48 citations recorded by the source corpus.

We establish two general nonlinear Liouville theorems for equations of the type −∆u = h(x1)f(u), u ≥ 0 in R , sup RN u < +∞. We then show how these Liouville theorems can be used to obtain a priori estimates for positive solutions of indefinite superlinear elliptic equations for several new cases left open in previous research.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9cc1b329dfef220a76714d96b797419f56e57ec2

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In Applied Mathematics

1. Patrick Winkert
2. Ky Ho
3. Leszek Gasinski
4. Nikolaos S. Papageorgiou
5. Vicentiu D. Rădulescu
6. Csaba Farkas

In Computational Theory and Mathematics

1. Patrick Winkert
2. Leszek Gasinski
3. Ky Ho
4. Nikolaos S. Papageorgiou
5. Vicentiu D. Rădulescu
6. Csaba Farkas

In Mathematical Physics

1. Patrick Winkert
2. Leszek Gasinski

Citations in the corpus

• L∞-Estimates for nonlinear elliptic Neumann boundary value problems (2010, background): “A priori estimates for the p−Laplacian equations with Dirichlet boundary values were also developed in [14], [26],[36],[39] and concerning the Laplace operator (p = 2) we refer to [5],[17],[19],[25].”