scholarly journals Positive least energy solutions for k-coupled critical systems involving fractional Laplacian

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xin Yin ◽  
Wenming Zou
Keyword(s):  
Fractional Laplacian ◽  
Critical Systems ◽  
Least Energy Solutions ◽  
Least Energy

Solutions for the Problems Involving Fractional Laplacian and Indefinite Potentials

2017 ◽  
Vol 17 (3) ◽  
Author(s):  
Zhongwei Tang ◽  
Lushun Wang
Keyword(s):  
Asymptotic Behavior ◽  
Fractional Laplacian ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Definition Of ◽  
Least Energy Solutions ◽  
Least Energy

AbstractIn this paper, we consider a class of Schrödinger equations involving fractional Laplacian and indefinite potentials. By modifying the definition of the Nehari–Pankov manifold, we prove the existence and asymptotic behavior of least energy solutions. As the fractional Laplacian is nonlocal, when the bottom of the potentials contains more than one isolated components, the least energy solutions may localize near all the isolated components simultaneously. This phenomenon is different from the Laplacian.

Least Energy Solutions with Sign Information for Parametric Double Phase Problems

2021 ◽  
Vol 77 (1) ◽  
Author(s):  
Nikolaos S. Papageorgiou ◽  
Calogero Vetro ◽  
Francesca Vetro
Keyword(s):  
Double Phase ◽  
Least Energy Solutions ◽  
Least Energy

scholarly journals The asymptotically linear Hénon problem

2020 ◽  
pp. 2050042
Author(s):  
Anna Lisa Amadori
Keyword(s):  
Boundary Conditions ◽  
Morse Index ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Radial Solutions ◽  
Asymptotically Linear ◽  
Planar Case ◽  
Asymptotic Profile ◽  
Least Energy Solutions ◽  
Least Energy

In this paper, we consider the Hénon problem in the ball with Dirichlet boundary conditions. We study the asymptotic profile of radial solutions and then deduce the exact computation of their Morse index when the exponent [Formula: see text] is close to [Formula: see text]. Next we focus on the planar case and describe the asymptotic profile of some solutions which minimize the energy among functions which are invariant for reflection and rotations of a given angle [Formula: see text]. By considerations based on the Morse index we see that, depending on the values of [Formula: see text] and [Formula: see text], such least energy solutions can be radial, or nonradial and different one from another.

Least Energy Solutions for Nonlinear Schrödinger Systems with Mixed Attractive and Repulsive Couplings

2015 ◽  
Vol 15 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Yohei Sato ◽  
Zhi-Qiang Wang
Keyword(s):  
Ground State ◽  
Nonlinear Elliptic System ◽  
Ground State Solutions ◽  
Nonlinear Elliptic ◽  
Asymptotic Profile ◽  
Nonlinear Schrödinger Systems ◽  
Schrödinger Systems ◽  
Bose Einstein ◽  
Least Energy Solutions ◽  
Least Energy

AbstractIn this paper we study the ground state solutions for a nonlinear elliptic system of three equations which comes from models in Bose-Einstein condensates. Comparing with existing works in the literature which have been on purely attractive or purely repulsive cases, our investigation focuses on the effect of mixed interaction of attractive and repulsive couplings. We establish the existence of least energy positive solutions and study asymptotic profile of the ground state solutions, giving indication of co-existence of synchronization and segregation. In particular we show symmetry breaking for the ground state solutions.

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