Multiple positive normalized solutions for nonlinear Schrödinger systems

Multiple Positive Solutions for Some Nonlinear Elliptic Systems

where k1, k2 > 0 are positive constants, Ω ⊂ R is a bounded domain with a smooth boundary ∂Ω and V (u, v) ∈ C(R,R). We refer to [CdFM], [CM], [dFF], [dFM] and [HvV] for variational study of such elliptic systems. However, it seems that the multiplicity of positive solutions for such elliptic systems is not well studied. Here, we study a case related to some models (with diffusion) in mathematic...

Multi-speed solitary wave solutions for nonlinear Schrödinger systems

Abstract. We prove the existence of a new type of solutions to a nonlinear Schrödinger system. These solutions, which we callmulti-speeds solitary waves, are behaving at large time as a couple of scalar solitary waves traveling at different speeds. The proof relies on the construction of approximations of the multi-speeds solitary waves by solving the system backwards in time and using energy m...

On a class of nonlinear fractional Schrödinger-Poisson systems

In this paper, we are concerned with the following fractional Schrödinger-Poisson system:    (−∆s)u + V (x)u + φu = m(x)|u|q−2|u|+ f(x,u), x ∈ Ω, (−∆t)φ = u2, x ∈ Ω, u = φ = 0, x ∈ ∂Ω, where s,t ∈ (0,1], 2t + 4s > 3, 1 < q < 2 and Ω is a bounded smooth domain of R3, and f(x,u) is linearly bounded in u at infinity. Under some assumptions on m, V and f we obtain the existence of non-trivial so...

Multiple Positive Solutions for Nonlinear Semipositone Fractional Differential Equations

Multiple Positive Solutions for Nonlinear Fractional Boundary Value Problems

This paper is devoted to the existence of multiple positive solutions for fractional boundary value problem DC0+αu(t)=f(t, u(t), u'(t)), 0<t<1, u(1)=u'(1)=u''(0)=0, where 2<α≤3 is a real number, DC0+α is the Caputo fractional derivative, and f:[0,1]×[0, +∞)×R→[0, +∞) is continuous. Firstly, by constructing a special cone, applying Guo-Krasnoselskii's fixed point theorem and Leggett-Williams fix...