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Multiple nodal solutions for elliptic equations

โœ Scribed by Aixia Qian; Shujie Li

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
295 KB
Volume
57
Category
Article
ISSN
0362-546X

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โœฆ Synopsis

We assert the locations of critical points constructed for the C 1 functional by the minimax method in terms of the order structures. These results are applied to nonlinear Dirichlet boundary value problems to obtain the multiplicity of nodal (sign-changing) solutions.

๐Ÿ“œ SIMILAR VOLUMES

Existence and Multiplicity of Nodal Solu
Existence and Multiplicity of Nodal Solutions for Nonlinear Elliptic Equations with Critical Sobolev Growth
โœ E. Hebey; M. Vaugon ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 594 KB

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 \(\Omega, u=0\)

Existence and Asymptotic-Behavior of Nod
Existence and Asymptotic-Behavior of Nodal Solutions for Semilinear Elliptic-Equations
โœ R. Kajikiya ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 533 KB

The elliptic equation \(\Delta u+f(u)=0\) in \(R^{n}\) is discussed in the case where \(f(u)=\) \(|u|^{n} \quad u(|u| \geqslant 1),=|u|^{4} \quad{ }^{1} u(|u|<1), 10\). It is further proved that for any \(k \geqslant 0\) there exist at least three radially symmetric solutions which have exactly \(k\