Results 51 to 60 of about 2,592,777 (103)

Planar Choquard equations with critical exponential reaction and Neumann boundary condition

Mathematische Nachrichten, Volume 297, Issue 10, Page 3847-3869, October 2024.
Abstract We study the existence of positive weak solutions for the following problem: −Δu+α(x)u=∫ΩF(y,u)|x−y|μ1dyf(x,u)inΩ,∂u∂η+βu=∫∂ΩG(y,u)|x−y|μ2dνg(x,u)on∂Ω,$$\begin{equation*} \begin{aligned} \hspace*{65pt}-\Delta u + \alpha (x) u &= {\left(\int \limits _{\Omega }\frac{F(y,u)}{|x-y|^{{\mu _1}}}\;dy\right)}f(x,u) \;\;\text{in} \; \Omega,\\ \hspace ...
Sushmita Rawat, Vicenţiu D. Rădulescu, K. Sreenadh   +2 more
wiley   +1 more source

Multiplicity Results of Solutions to the Fractional p-Laplacian Problems of the Kirchhoff–Schrödinger–Hardy Type

Mathematics
This paper is devoted to establishing multiplicity results of nontrivial weak solutions to the fractional p-Laplacian equations of the Kirchhoff–Schrödinger type with Hardy potentials.
Yun-Ho Kim
doaj   +1 more source

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

Asymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equations [PDF]

, 2014
preprintIn this paper, we analyze the asymptotic behavior of Palais-Smale sequences associated to fractional Yamabe type equations on an asymptotically hyperbolic Riemannian manifold.
María del Mar González Nogueras, González Nogueras, María del Mar, Yi Fang, Fang, Yi   +3 more
core   +2 more sources

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

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  

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

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  

Multiple solutions for nonlinear discontinuous strongly resonant elliptic problems

Abstract and Applied Analysis, 2000
We consider quasilinear strongly resonant problems with discontinuous right-hand side. To develop an existence theory we pass to a multivalued problem by, roughly speaking, filling in the gaps at the discontinuity points.
Nikolaos C. Kourogenis, Nikolaos S. Papageorgiou   +1 more
doaj   +1 more source