Results 31 to 40 of about 218 (139)
A generalization of Ekeland's variational principle with applications
Electronic Journal of Differential Equations, 2006 In this paper, we establish a variant of Ekeland's variational principle. This result suggest to introduce a generalization of the famous Palais-Smale condition.
Abdel R. El Amrouss, Najib Tsouli
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Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1783-1842, September 2025.Abstract We consider the global dynamics of finite energy solutions to energy‐critical equivariant harmonic map heat flow (HMHF) and radial nonlinear heat equation (NLH). It is known that any finite energy equivariant solutions to (HMHF) decompose into finitely many harmonic maps (bubbles) separated by scales and a body map, as approaching to the ...
Kihyun Kim, Frank Merle
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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
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Infinitely many homoclinic solutions for a class of damped vibration problems
Electronic Journal of Qualitative Theory of Differential Equations, 2022 In this paper, we consider the multiplicity of homoclinic solutions for the following damped vibration problems $$ \ddot{x}(t)+B\dot{x}(t)-A(t)x(t)+H_{x}(t,x(t))=0,$$ where $A(t)\in (\mathbb{R},\mathbb{R}^{N})$ is a symmetric matrix for all $t\in \mathbb{
Huijuan Xu, Shan Jiang, Guanggang Liu
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Mathematische Nachrichten, Volume 298, Issue 8, Page 2570-2595, August 2025.Abstract We discuss the existence theory of a nonlinear problem of nonlocal type subject to Neumann boundary conditions. Differently from the existing literature, the elliptic operator under consideration is obtained as a superposition of operators of mixed order. The setting that we introduce is very general and comprises, for instance, the sum of two
Serena Dipierro +3 more
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Infinitely many solutions to critical problems involving the p-Grushin operator
Electronic Journal of Differential EquationsWe consider a critical problem in a bounded domain involving the p-Grushin operator. After a truncation argument, we obtain infinitely many solutions to our problem via Krasnoselskii's genus, extending a previous result of Garcia Azorero and Peral Alonso
Paolo Malanchini +2 more
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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 +3 more
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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
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
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A version of Zhong's coercivity result for a general class of nonsmooth functionals
Abstract and Applied Analysis, 2002 A version of Zhong's coercivity result (1997) is established for nonsmooth functionals expressed as a sum Φ+Ψ, where Φ is locally Lipschitz and Ψ is convex, lower semicontinuous, and proper.
D. Motreanu, V. V. Motreanu, D. Paşca
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