Abstract
In this paper the mountain--pass theorem and the Ekeland variationalprinciple in a suitable Orlicz space are employed to establish theexistence of positive standing wave solutions for a quasilinearSchrödinger equation involving a combination of concave andconvex terms. The second order nonlinearity considered in this papercorresponds to the superfluid equation in plasma physics.
Highlights
In this paper we are concerned with quasilinear Schrodinger equations of the form ∂ψ i= −∆ψ + W (x)ψ − η(|ψ|2)ψ − κ ∆ρ(|ψ|2) ρ (|ψ|2)ψ, (1)∂t where ψ : R × RN → C, κ is a positive constant, W : RN → R is a given potential and ρ, η : R+ → R are suitable functions
In this paper the mountain–pass theorem and the Ekeland variational principle in a suitable Orlicz space are employed to establish the existence of positive standing wave solutions for a quasilinear Schrodinger equation involving a combination of concave and convex terms
The second order nonlinearity considered in this paper corresponds to the superfluid equation in plasma physics
Summary
In this paper we are concerned with quasilinear Schrodinger equations of the form ∂ψ i= −∆ψ + W (x)ψ − η(|ψ|2)ψ − κ ∆ρ(|ψ|2) ρ (|ψ|2)ψ, (1)∂t where ψ : R × RN → C, κ is a positive constant, W : RN → R is a given potential and ρ, η : R+ → R are suitable functions. QUASILINEAR SCHRO DINGER EQUATIONS INVOLVING CONCAVE AND CONVEX NONLINEARITIES Departamento de Matematica Universidade Federal da Paraıba 58051-900, Joao Pessoa – PB – Brazil (Communicated by Zhi-Qiang Wang)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.