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2 results

On the classification of standing wave solutions to a coupled Schrödinger system
Part of
- Elliptic equations and systems
- Partial differential equations
Zhi-You Chen, Yu-Jen Huang, Yong-Li Tang
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 149 / Issue 5 / October 2019

Published online by Cambridge University Press:

17 January 2019, pp. 1347-1370

Print publication:

October 2019
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In this paper, we consider a nonlinear elliptic system which is an extension of the single equation derived by investigating the stationary states of the nonlinear Schrödinger equation. We establish the existence and uniqueness of solutions to the Dirichlet problem on the ball and entire space as the parameters within certain regions. In addition, a complete structure of different types of solutions for the radial case is also provided.

A result of multiplicity of solutions for a class of quasilinear equations
Part of
Claudianor O. Alves, Giovany M. Figueiredo, Uberlandio B. Severo
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 55 / Issue 2 / June 2012

Published online by Cambridge University Press:

23 February 2012, pp. 291-309
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We establish the multiplicity of positive weak solutions for the quasilinear Dirichlet problem −Lpu + |u|p−2u = h(u) in Ωλ, u = 0 on ∂Ωλ, where Ωλ = λΩ, Ω is a bounded domain in ℝN, λ is a positive parameter, Lpu ≐ Δpu + Δp(u2)u and the nonlinear term h(u) has subcritical growth. We use minimax methods together with the Lyusternik–Schnirelmann category theory to get multiplicity of positive solutions.

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2 results

On the classification of standing wave solutions to a coupled Schrödinger system

A result of multiplicity of solutions for a class of quasilinear equations