Results 61 to 70 of about 3,788 (155)

Least energy solutions for a class of (p1,p2)$(p_{1}, p_{2})$‐Kirchhoff‐type problems in RN$\mathbb {R}^{N}$ with general nonlinearities

Journal of the London Mathematical Society, Volume 110, Issue 4, October 2024.
Abstract We examine the following (p1,p2)$(p_{1}, p_{2})$‐Kirchhoff‐type problem: −M1∥∇u∥Lp1(RN)p1Δp1u−M2∥∇u∥Lp2(RN)p2Δp2u=g(u)inRN,u∈W1,p1(RN)∩W1,p2(RN),$$\begin{equation*} {\left\lbrace \def\eqcellsep{&}\begin{array}{ll}-M_{1}\left(\Vert \nabla u\Vert ^{p_{1}}_{L^{p_{1}}(\mathbb {R}^{N})}\right)\Delta _{p_{1}}u-M_{2}\left(\Vert \nabla u\Vert ^{p_{2 ...
Vincenzo Ambrosio
wiley   +1 more source

Generalized noncooperative Schrödinger–Kirchhoff–type systems in RN$\mathbb {R}^N$

Mathematische Nachrichten, Volume 297, Issue 6, Page 2092-2121, June 2024.
Abstract We consider a class of noncooperative Schrödinger–Kirchhof–type system, which involves a general variable exponent elliptic operator with critical growth. Under certain suitable conditions on the nonlinearities, we establish the existence of infinitely many solutions for the problem by using the limit index theory, a version of concentration ...
Nabil Chems Eddine, Dušan D. Repovš
wiley   +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

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
wiley   +1 more source

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
wiley   +1 more source

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  

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
wiley   +1 more source

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
doaj  

Solvability of a Class of Fractional Advection–Dispersion Coupled Systems

Mathematics
The 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
doaj   +1 more source