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Infinitely many solutions for three classes of self-similar equations with p-Laplace operator: Gelfand, Joseph–Lundgren and MEMS problems

Part of: Partial differential equations Elliptic equations and systems

Published online by Cambridge University Press:  17 October 2017

Philip Korman
Philip Korman*
Affiliation:
Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221-0025, USA (kormanp@ucmail.uc.edu)
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Abstract

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We study global solution curves and prove the existence of infinitely many positive solutions for three classes of self-similar equations with p-Laplace operator. In the p = 2 case these are well-known problems involving the Gelfand equation, the equation modelling electrostatic micro-electromechanical systems (MEMS), and a polynomial nonlinearity. We extend the classical results of Joseph and Lundgren to the case in which p ≠ 2, and we generalize the main result of Guo and Wei on the equation modelling MEMS.

Keywords

parametrization of the global solution curvesinfinitely many solutions

MSC classification

Secondary: 35J60: Nonlinear elliptic equations 35B40: Asymptotic behavior of solutions
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 2 , April 2018 , pp. 341 - 356
Copyright
Copyright © Royal Society of Edinburgh 2018