Results 61 to 70 of about 3,762 (154)
Periodic Solutions of Classical Hamiltonian Systems without Palais–Smale Condition
Journal of Mathematical Analysis and Applications, 2002 The authors consider the second order Hamiltonian system \(\ddot{u}+V_u(t,u)=0\) where \(V:\mathbb R\times\mathbb R^N\rightarrow\mathbb R\) is \({\mathcal{C}}^2\), \(T\)-periodic in \(t\), and \(V_u\) is globally bounded. Further conditions on \(V\) for \(|u|\rightarrow\infty\) are not required.
Fei, Guihua +2 more
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Multiplicity‐1 minmax minimal hypersurfaces in manifolds with positive Ricci curvature
Communications on Pure and Applied Mathematics, Volume 77, Issue 3, Page 2081-2137, March 2024.Abstract We address the one‐parameter minmax construction for the Allen–Cahn energy that has recently lead to a new proof of the existence of a closed minimal hypersurface in an arbitrary compact Riemannian manifold Nn+1$N^{n+1}$ with n≥2$n\ge 2$ (Guaraco's work, relying on works by Hutchinson, Tonegawa, and Wickramasekera when sending the Allen–Cahn ...
Costante Bellettini
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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 ...
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Almost monotonicity formula for H‐minimal Legendrian surfaces in the Heisenberg group
Communications on Pure and Applied Mathematics, Volume 77, Issue 3, Page 1940-1957, March 2024.Abstract We prove an almost monotonicity formula for H‐minimal Legendrian Surfaces (also called contact stationary Legendrian immersions or Hamiltonian stationary immersions) in the Heisenberg Group H2${\mathbb {H}}^2$. From this formula we deduce a Bernstein‐Liouville type theorem for H‐minimal Legendrian Surfaces.
Tristan Rivière
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Equivariant Lagrangian Floer homology via cotangent bundles of EGN$EG_N$
Journal of Topology, Volume 17, Issue 1, March 2024.Abstract We provide a construction of equivariant Lagrangian Floer homology HFG(L0,L1)$HF_G(L_0, L_1)$, for a compact Lie group G$G$ acting on a symplectic manifold M$M$ in a Hamiltonian fashion, and a pair of G$G$‐Lagrangian submanifolds L0,L1⊂M$L_0, L_1 \subset M$.
Guillem Cazassus
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An existence result for hemivariational inequalities
Electronic Journal of Differential Equations, 2004 We present a general method for obtaining solutions for an abstract class of hemivariational inequalities. This result extends many results to the nonsmooth case. Our proof is based on a nonsmooth version of the Mountain Pass Theorem with Palais-Smale or
Zsuzsanna Dalyay, Csaba Varga
doaj
Non‐autonomous double phase eigenvalue problems with indefinite weight and lack of compactness
Bulletin of the London Mathematical Society, Volume 56, Issue 2, Page 734-755, February 2024.Abstract In this paper, we consider eigenvalues to the following double phase problem with unbalanced growth and indefinite weight, −Δpau−Δqu=λm(x)|u|q−2uinRN,$$\begin{equation*} \hspace*{3pc}-\Delta _p^a u-\Delta _q u =\lambda m(x)|u|^{q-2}u \quad \mbox{in} \,\, \mathbb {R}^N, \end{equation*}$$where N⩾2$N \geqslant 2$, 1
Tianxiang Gou, Vicenţiu D. Rădulescu
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Nontrivial solutions for noncooperative elliptic systems at resonance
Electronic Journal of Differential Equations, 2001 In this article we establish the existence of a nonzero solution for variational noncooperative elliptic systems under Dirichlet boundary conditions and a resonant condition at infinity.
Elves A. B. Silva
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Solvability of a Class of Fractional Advection–Dispersion Coupled Systems
MathematicsThe purpose of this study is to provide some criteria for the existence and multiplicity of solutions for a class of fractional advection–dispersion coupled systems with nonlinear Sturm–Liouville conditions and instantaneous and non-instantaneous ...
Yan Qiao, Tao Lu
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The Morse Index of Sacks–Uhlenbeck α‐Harmonic Maps for Riemannian Manifolds
Journal of Mathematics, Volume 2024, Issue 1, 2024.In this paper, first we prove a nonexistence theorem for α‐harmonic mappings between Riemannian manifolds. Second, the instability of nonconstant α‐harmonic maps is studied with regard to the Ricci curvature criterion of their codomain. Then, we estimate the Morse index for measuring the degree of instability of some particular α‐harmonic maps ...
Amir Shahnavaz +3 more
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