Infinitely many solutions for three classes of self-similar equations with p-Laplace operator: Gelfand, Joseph–Lundgren and MEMS problems
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-electromechani...
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Veröffentlicht in: | Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2018-04, Vol.148 (2), p.341-356 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | 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. |
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ISSN: | 0308-2105 1473-7124 |
DOI: | 10.1017/S0308210517000038 |