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Existence and Multiplicity of Nodal Solutions for Nonlinear Elliptic Equations with Critical Sobolev Growth

โœ Scribed by E. Hebey; M. Vaugon

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
594 KB
Volume
119
Category
Article
ISSN
0022-1236

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โœฆ Synopsis

Let (\Omega) be a smooth bounded domain of (\mathbb{R}^{n}, n \geqslant 3), and let (a(x)) and (f(x)) be two smooth functions defined on a neighbourhood of (\Omega). First we study the existence of nodal solutions for the equation (\Delta u+a(x) u=f(x)|u|^{4 /(n-2)} u) on (\Omega, u=0) on (\partial \Omega). In particular, when (\Omega) is a solid torus of (\mathbb{R}^{3}), we describe three infinity (of pairs) of solutions of the equation (\Delta u=|u|^{4 / n-2)} u) on (\Omega, u=0) on (\partial \Omega). Afterwards, we study the equation when the zero Dirichlet condition on the boundary is replaced by a non-zero Dirichlet condition. 1994 Academic Press. Inc.

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