Results 41 to 50 of about 1,002 (168)

Failure of Plais-Smale condition and blow-up analysis for the critical exponent problem in R² [PDF]

, 1997
Let Ω be a bounded smooth domain inR2. Letf:R→R be a smooth non-linearity behaving like exp{s2} ass→∞. LetF denote the primitive off. Consider the functionalJ:H01(Ω)→R given by J(u)=12∫Ω|∇u|2dx−∫ΩF(u)dx.
Adimurthi, ., Prashanth, S.
core   +1 more source

Homoclinic Solutions of Nonlinear Laplacian Difference Equations Without Ambrosetti-Rabinowitz Condition [PDF]

, 2021
The aim of this paper is to establish the existence of at least two non-zero homoclinic solutions for a nonlinear Laplacian difference equation without using Ambrosetti-Rabinowitz type-conditions. The main tools are mountain pass theorem and Palais-Smale
Tersian S., Nastasi A., Vetro C.
core   +1 more source

Existence of Normalized Solutions of a Hartree–Fock System With Mass Subcritical Growth

Mathematical Methods in the Applied Sciences, Volume 48, Issue 12, Page 12309-12319, August 2025.
ABSTRACT In this paper, we are concerned with normalized solutions of a class of Hartree‐Fock type systems. By seeking the constrained global minimizers of the corresponding functional, we prove that the existence and nonexistence of normalized solutions.
Hua Jin, Yanyun Chang, Marco Squassina, Jianjun Zhang   +3 more
wiley   +1 more source

Diffeomorphisms of 4‐manifolds from graspers

Proceedings of the London Mathematical Society, Volume 131, Issue 1, July 2025.
Abstract We relate degree one grasper families of embedded circles to various constructions of diffeomorphisms found in the literature, theta clasper classes of Watanabe, barbell diffeomorphisms of Budney and Gabai, and twin twists of Gay and Hartman. We use a ‘parametrised surgery map’ that for a smooth 4‐manifold M$M$ takes loops of framed embeddings
Danica Kosanović
wiley   +1 more source

Positive ground states for nonlinear Schrödinger–Kirchhoff equations with periodic potential or potential well in R 3 $\mathbf{R}^{3}$

Boundary Value Problems, 2022
This work is devoted to the nonlinear Schrödinger–Kirchhoff-type equation − ( a + b ∫ R 3 | ∇ u | 2 d x ) Δ u + V ( x ) u = f ( x , u ) , in  R 3 , $$ - \biggl( a+b \int _{\mathbb{R}^{3}} \vert \nabla u \vert ^{2} \,\text{d}x \biggr) \Delta u+V(x)u=f(x,u)
Wei Chen, Zunwei Fu, Yue Wu
doaj   +1 more source

Spectrum of a Self-Adjoint Operator and Palais-Smale Conditions [PDF]

Journal of the London Mathematical Society, 2000
Let \(S\) be a bounded or unbounded self-adjoint operator in a real Hilbert space \((H,\langle\cdot, \cdot\rangle)\). The first result states that \(S\) gives rise to unique bounded linear operators \(A\) and \(L\) in the form domain \(H_1= D(|S|^{1/2})\) of \(S\) equipped with its natural scalar product \[ \langle u,v\rangle_1:= \langle u,v\rangle ...
openaire   +1 more source

Ground State Solutions for General Choquard Equation With the Riesz Fractional Laplacian

Advances in Mathematical Physics, Volume 2025, Issue 1, 2025.
In this work, we study the existence of a nonzero solution for the following nonlinear general Choquard equation (CE): −Δν+ν=−ΔD−α2 ∗ Fνfν,in ℝN, where N ≥ 3, F represents the primitive function of f, f∈CR;R is a function that fulfils the general Berestycki–Lions conditions, ΔD denotes the Laplacian operator on Ω with zero Dirichlet boundary conditions
Sarah Abdullah Qadha, Muneera Abdullah Qadha, Haibo Chen, Yuying Zao, Kang-Jia Wang   +4 more
wiley   +1 more source

Subsonic periodic traveling waves in Fermi–Pasta–Ulam type systems with nonlocal interaction on 2d-lattice

Математичні Студії
The paper is devoted to Fermi--Pasta--Ulam type system that describe an infinite system of nonlinearly coupled particles with nonlocal interaction on a two dimensional integer-valued lattice.
S. M. Bak, H. M. Kovtoniuk
doaj   +1 more source

Concentration–Compactness Principle to a Weighted Moser–Trudinger Inequality and Its Application

Journal of Mathematics, Volume 2025, Issue 1, 2025.
We employ level‐set analysis of functions to establish a sharp concentration–compactness principle for the Moser–Trudinger inequality with power weights in R+2. Furthermore, we systematically prove the existence of ground state solutions to the associated nonlinear partial differential equation.
Yubo Ni, Agacik Zafer
wiley   +1 more source

Existence and Nonexistence of Periodic Solutions for a Class of Fourth‐Order Partial Difference Equations

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this paper, we investigate multiplicity, existence, and nonexistence of periodic solutions to a fourth‐order partial difference equation via linking theorem and saddle point theorem. Our obtained results significantly generalize and improve some existing ones.
Dan Li, Yuhua Long, Ji Gao
wiley   +1 more source