Double phase problems with competing potentials: concentration and multiplication of ground states

J Zhang, W Zhang, VD Rădulescu - Mathematische Zeitschrift, 2022 - Springer
In this paper, we establish concentration and multiplicity properties of ground state solutions
to the following perturbed double phase problem with competing potentials:-ϵ p Δ pu-ϵ q Δ …

[图书][B] Singularly perturbed methods for nonlinear elliptic problems

D Cao, S Peng, S Yan - 2021 - books.google.com
This introduction to the singularly perturbed methods in the nonlinear elliptic partial
differential equations emphasises the existence and local uniqueness of solutions exhibiting …

Spikes in two coupled nonlinear Schrödinger equations

TC Lin, J Wei - Annales de l'Institut Henri Poincaré C, Analyse non …, 2005 - Elsevier
Here we study the interaction and the configuration of spikes in a double condensate by
analyzing least energy solutions of two coupled nonlinear Schrödinger equations which …

Choquard-type equations with Hardy–Littlewood–Sobolev upper-critical growth

D Cassani, J Zhang - Advances in Nonlinear Analysis, 2018 - degruyter.com
We are concerned with the existence of ground states and qualitative properties of solutions
for a class of nonlocal Schrödinger equations. We consider the case in which the …

[PDF][PDF] Semi-classical states of nonlinear Schrödinger equations: a variational reduction method

M Del Pino, P Felmer - Mathematische Annalen, 2002 - capde.cmm.uchile.cl
Mathematische Annalen Page 1 Digital Object Identifier (DOI) 10.1007/s002080200327 Math.
Ann. 324, 1–32 (2002) Mathematische Annalen Semi-classical states of nonlinear Schrödinger …

Concentration phenomena for the nonlocal Schrödinger equation with Dirichlet datum

J Dávila, M Del Pino, S Dipierro, E Valdinoci - Analysis & PDE, 2015 - msp.org
Concentration phenomena for the nonlocal Schrödinger equation with Dirichlet datum Page 1
ANALYSIS & PDE msp Volume 8 No. 5 2015 JUAN DÁVILA, MANUEL DEL PINO, SERENA …

On the number of interior peak solutions for a singularly perturbed Neumann problem

FH Lin, WM Ni, JC Wei - … on Pure and Applied Mathematics: A …, 2007 - Wiley Online Library
We consider the following singularly perturbed Neumann problem: ϵ^ 2 Δ u-u+ f (u)=
0\enspace\rm in\Omega,\quad\it u>\rm 0\enspace\rm in\Omega, ∂\it u ∂ ν= 0\enspace\rm …

Point dynamics in a singular limit of the Keller--Segel model 1: Motion of the concentration regions

JJL Velázquez - SIAM Journal on Applied Mathematics, 2004 - SIAM
The purpose of this paper is to study a singular perturbation limit of a Keller--Segel system
that generates blow-up in finite time. The main question that is addressed is the description …

Hamiltonian elliptic systems: a guide to variational frameworks

D Bonheure, EM dos Santos, H Tavares - Portugaliae Mathematica, 2014 - ems.press
Hamiltonian elliptic systems: a guide to variational frameworks Page 1 Portugal. Math. (NS)
Portugaliae Mathematica Vol. 71, Fasc. 3-4, 2014, 301–395 6 European Mathematical Society …

Normalized solutions for (p, q)-Laplacian equations with mass supercritical growth

L Cai, VD Rădulescu - Journal of Differential Equations, 2024 - Elsevier
In this paper, we study the following (p, q)-Laplacian equation with L p-constraint:{− Δ pu− Δ
q u+ λ| u| p− 2 u= f (u), in RN,∫ RN| u| pdx= cp, u∈ W 1, p (RN)∩ W 1, q (RN), where 1< p< …