Least energy solutions for a weakly coupled fractional Schrödinger system

2016 ◽  
Vol 132 ◽  
pp. 141-159 ◽  
Author(s):  
Qing Guo ◽  
Xiaoming He
Keyword(s):  
Weakly Coupled ◽  
Least Energy Solutions ◽  
Least Energy ◽  
Schrödinger System

scholarly journals Phase Separation, Optimal Partitions, and Nodal Solutions to the Yamabe Equation on the Sphere

2020 ◽  
Author(s):  
Mónica Clapp ◽  
Alberto Saldaña ◽  
Andrzej Szulkin
Keyword(s):  
Optimal Partition ◽  
Partition Problem ◽  
Round Sphere ◽  
Nodal Solutions ◽  
Nodal Domains ◽  
Optimal Partitions ◽  
Yamabe Equation ◽  
Weakly Coupled ◽  
Least Energy Solutions ◽  
Least Energy

Abstract We study an optimal $M$-partition problem for the Yamabe equation on the round sphere, in the presence of some particular symmetries. We show that there is a correspondence between solutions to this problem and least energy sign-changing symmetric solutions to the Yamabe equation on the sphere with precisely $M$ nodal domains. The existence of an optimal partition is established through the study of the limit profiles of least energy solutions to a weakly coupled competitive elliptic system on the sphere.

scholarly journals Ground state solution of semilinear Schrödinger system with local super-quadratic conditions

2021 ◽  
pp. 1-18
Author(s):  
Jing Chen ◽  
Yiqing Li
Keyword(s):  
Variational Method ◽  
Ground State ◽  
Ground State Solution ◽  
State Solution ◽  
The Other ◽  
Ground State Solutions ◽  
Approximation Argument ◽  
Least Energy Solutions ◽  
Least Energy ◽  
Schrödinger System

In this paper, we dedicate to studying the following semilinear Schrödinger system equation*-Δu+V1(x)u=Fu(x,u,v)amp;mboxin~RN,r-Δv+V2(x)v=Fv(x,u,v)amp;mboxin~RN,ru,v∈H1(RN),endequation* where the potential Vi are periodic in x,i=1,2, the nonlinearity F is allowed super-quadratic at some x ∈ R N and asymptotically quadratic at the other x ∈ R N . Under a local super-quadratic condition of F, an approximation argument and variational method are used to prove the existence of Nehari–Pankov type ground state solutions and the least energy solutions.

scholarly journals Critical polyharmonic systems and optimal partitions

2021 ◽  
Vol 20 (11) ◽  
pp. 3991
Author(s):  
Mónica Clapp ◽  
Juan Carlos Fernández ◽  
Alberto Saldaña
Keyword(s):  
Existence Of Solutions ◽  
Optimal Partition ◽  
Partition Problem ◽  
Competitive System ◽  
Polyharmonic Equations ◽  
Optimal Partitions ◽  
Weakly Coupled ◽  
Coupling Parameters ◽  
Least Energy Solutions ◽  
Least Energy

<p style='text-indent:20px;'>We establish the existence of solutions to a weakly-coupled competitive system of polyharmonic equations in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^N $\end{document}</tex-math></inline-formula> which are invariant under a group of conformal diffeomorphisms, and study the behavior of least energy solutions as the coupling parameters tend to <inline-formula><tex-math id="M2">\begin{document}$ -\infty $\end{document}</tex-math></inline-formula>. We show that the supports of the limiting profiles of their components are pairwise disjoint smooth domains and solve a nonlinear optimal partition problem of <inline-formula><tex-math id="M3">\begin{document}$ \mathbb R^N $\end{document}</tex-math></inline-formula>. We give a detailed description of the shape of these domains.</p>

Sign in / Sign up

Export Citation Format

Share Document