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Existence of singular
positive solutions for some semilinear elliptic equations
Zongming Guo, Dong Ye and Feng Zhou |
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Vol. 236 (2008), No. 1, 57–71
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Abstract |
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We study positive solutions of an equation with singular nonlinearities. The equation arises in the study of equilibrium states of thin films. Under weak assumptions on the nonlinearity, we show that for N ≥ 3 there exists a family of radial solutions {uα}α>0 with uα(0) = α and each of them is oscillatory in (0,∞). We obtain then a singular radial solution in (0,∞) by taking the limit α → 0. Meanwhile, using the solutions obtained in (0,∞), we show some existence results for the corresponding Neumann eigenvalue problem on a ball. |
Keywords
elliptic equation with singular nonlinearity, rupture
solutions, oscillation
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Mathematical Subject Classification 2000
Primary: 35J60, 35B45, 35B05
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Milestones
Received: 11 May 2007
Revised: 27 September 2007
Accepted: 25 February 2008
Published: 1 May 2008
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Authors |
| Zongming Guo | |
| Department of Mathematics Henan Normal University Xinxiang 453002 China |
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| Dong Ye | |
| Département de Mathématiques, UMR
8088 Université de Cergy-Pontoise Site Saint-Martin, BP 222 95302 Cergy-Pontoise Cedex France |
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| Feng Zhou | |
| Department of Mathematics East China Normal University Shanghai 200062 China |
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