Large and Small Solutions of a Class of Quasilinear Elliptic Eigenvalue Problems

By Zongming Guo, J. Webb. 2002

68 citations recorded by the source corpus.

Abstract Existence and uniqueness results for large positive solutions are obtained for a class of quasilinear elliptic eigenvalue problems in general bounded smooth domains via a generalization of a sweeping principle of Serrin. The nonlinear terms of the problems can be negative in some intervals. The existence and structure of a mountain pass solution are also discussed. We show that this solution develops to a spike layer solution.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/9665a9e3241bf9ff070ee301e8a491a657f0f4f5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Zongming Guo
2. Yihong Du
3. Mingxin Wang
4. Ahmed Mohammed
5. Rui Peng
6. Yanyan Li
7. Lei Zhang
8. Yuan Lou

In Computational Theory and Mathematics

1. Yihong Du
2. Zongming Guo
3. Ahmed Mohammed
4. Zhijun Zhang
5. Yanyan Li
6. Lei Zhang
7. Frank No'e
8. Hao Wu

In Control and Systems Engineering

1. Yihong Du
2. Zongming Guo
3. Zhijun Zhang

Citations in the corpus

• Liouville type results and eventual flatness of positive solutions for $p$-Laplacian equations (2002, result): “We only mention [3, 4, 5, 14, 15, 16, 17, 18, 19, 21, 31] for some relatively recent results.”