Results 41 to 50 of about 3,788 (155)

ON THE PALAIS-SMALE CONDITION FOR NONDIFFERENTIABLE FUNCTIONALS

Taiwanese Journal of Mathematics, 2000
In this paper the author studies the relations between some extensions to nonsmooth functionals of the classical Palais-Smale (PS) compactness condition for smooth functionals. In particular the relations between some results of K. C. Chang and other results by Costa and Goncalves are presented.
openaire   +2 more sources

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

Some properties of Palais-Smale sequences with applications to elliptic boundary-value problems

Electronic Journal of Differential Equations, 1999
When using calculus of variations to study nonlinear elliptic boundary-value problems on unbounded domains, the Palais-Smale condition is not always satisfied.
Chao-Nien Chen, Shyuh-Yaur Tzeng
doaj  

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

Existence of groundstates for a class of nonlinear Choquard equations in the plane

, 2017
We prove the existence of a nontrivial groundstate solution for the class of nonlinear Choquard equation $$ -\Delta u+u=(I_\alpha*F(u))F'(u)\qquad\text{in }\mathbb{R}^2, $$ where $I_\alpha$ is the Riesz potential of order $\alpha$ on the plane $\mathbb{R}
Battaglia, Luca, Van Schaftingen, Jean
core   +1 more source

Curve-straightening and the Palais-Smale condition [PDF]

Transactions of the American Mathematical Society, 1998
This paper considers the negative gradient trajectories associated with the modified total squared curvature functional ∫ k 2 + ν d s \int k^{2} +\nu ds . The focus is on the limiting behavior as ν \nu tends to zero from the positive
openaire   +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

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