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Asymmetric solutions for symmetric problems arising in nonlinear optics

✍ Scribed by Silvia Cingolani

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
434 KB
Volume
47
Category
Article
ISSN
0362-546X

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✦ Synopsis

Existence of asymmetric positive solutions for a class of symmetric nonlinear elliptic equations in (\mathbb{R}^{N}, N \geq 1) has been proved by using variational arguments. In the one-dimensional case such equation is a model in Nonlinear Optics aring in the study of asymmetric guided waves in a stratified dielectric medium. In dimension (N=2) the equation is a scalar approximation of a model arising from the study of propagation of a monochromatic electric field in optical cylindrical waveguides.

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Symmetric positive solutions for nonline
Symmetric positive solutions for nonlinear boundary value problems with -Laplacian operator
✍ Yan Luo; Zhiguo Luo πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 302 KB

This paper proves the existence, multiplicity, and nonexistence of symmetric positive solutions to nonlinear boundary value problems with Laplacian operator. We improve and generalize some relative results. Our analysis mainly relies on the fixed point theorem of cone expansion and compression of no