Nodal Solutions of a p-Laplacian Equation |
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| Authors: | Bartsch, Thomas Liu, Zhaoli Weth, Tobias |
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| Affiliation: | Mathematisches Institut, Universität Giessen Arndtstrasse 2, 35392 Giessen, Germany. E-mail: Thomas.Bartsch{at}math.uni-giessen.de, Tobias.Weth{at}math.uni-giessen.de
Department of Mathematics, Capital Normal University Beijing 100037, P. R. China. E-mail: zliu{at}mail.cnu.edu.cn |
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| Abstract: | We prove that the p-Laplacian problem  p u = f(x, u),with u   on a bounded domain   RN, with p > 1 arbitrary, has a nodal solution providedthat f : x R  R is subcritical, and f(x, t) / |t|p 2 is superlinear. Infinitely many nodal solutions are obtainedif, in addition, f(x, t) = f(x, t). 2000 MathematicsSubject Classification 35J20, 35J65, 58E05. |
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| Keywords: | p-Laplacian equation superlinear non-linearity nodal solution variational method invariant set of descending flow |
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