Symmetry of n-mode positive solutions for two-dimensional H\'enon type systems
, 2013 We provide a symmetry result for n-mode positive solutions of a general class of semi-linear elliptic systems under cooperative conditions on the nonlinearities.
Shioji, Naoki, Squassina, Marco
core
Symmetry of n-mode positive solutions for two-dimensional Hénon type systems [PDF]
arXiv, 2013 We provide a symmetry result for n-mode positive solutions of a general class of semi-linear elliptic systems under cooperative conditions on the nonlinearities. Moreover, we apply the result to a class of H\'enon systems and provide the existence of multiple n-mode positive solutions.
arxiv
Hopf's lemmas for parabolic fractional Laplacians and parabolic fractional $p$-Laplacians [PDF]
arXiv, 2020 In this paper, we first establish Hopf's lemmas for parabolic fractional equations and parabolic fractional $p$-equations. Then we derive an asymptotic Hopf's lemma for antisymmetric solutions to parabolic fractional equations. We believe that these Hopf's lemmas will become powerful tools in obtaining qualitative properties of solutions for nonlocal ...
arxiv
Normalized solutions for the double-phase problem with nonlocal reaction
Advances in Nonlinear AnalysisIn this article, we consider the double-phase problem with nonlocal reaction. For the autonomous case, we introduce the methods of the Pohozaev manifold, Hardy-Littlewood Sobolev subcritical approximation, adding the mass term to prove the existence and ...
Cai Li, Zhang Fubao
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Nonexistence results for elliptic differential inequalities with a potential on Riemannian manifolds [PDF]
arXiv, 2014 In this paper we are concerned with a class of elliptic differential inequalities with a potential both on $\erre^m$ and on Riemannian manifolds. In particular, we investigate the effect of the geometry of the underlying manifold and of the behavior of the potential at infinity on nonexistence of nonnegative solutions.
arxiv
Concentration phenomena for a fractional relativistic Schrödinger equation with critical growth
Advances in Nonlinear AnalysisIn this paper, we are concerned with the following fractional relativistic Schrödinger equation with critical growth: (−Δ+m2)su+V(εx)u=f(u)+u2s*−1inRN,u∈Hs(RN),u>0inRN,\left\{\begin{array}{ll}{\left(-\Delta +{m}^{2})}^{s}u+V\left(\varepsilon x)u=f\left(u)
Ambrosio Vincenzo
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Asymptotics of ground states for fractional Hénon systems [PDF]
arXiv, 2014 We investigate the asymptotic behavior of positive ground states for H\'enon type systems involving a fractional Laplacian on a bounded domain, when the powers of the nonlinearity approach the Sobolev critical exponent.
arxiv
An indefinite concave-convex equation under a Neumann boundary condition II
, 2016 We proceed with the investigation of the problem $(P_\lambda): $ $-\Delta u = \lambda b(x)|u|^{q-2}u +a(x)|u|^{p-2}u \ \mbox{ in } \Omega, \ \ \frac{\partial u}{\partial \mathbf{n}} = 0 \ \mbox{ on } \partial \Omega$, where $\Omega$ is a bounded smooth ...
Quoirin, Humberto Ramos +1 more
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A uniqueness result for the fractional Schrödinger-Poisson system with strong singularity
Open MathematicsThis article considers existence of solution for a class of fractional Schrödinger-Poisson system. By using the Nehari method and the variational method, we obtain a uniqueness result for positive solutions.
Wang Li +4 more
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Convexity and concavity of the ground state energy [PDF]
New York J. Math. 21 (2015) 1003-1005, 2015 This note proves convexity resp. concavity of the ground state energy of one dimensional Schr\"odinger operators as a function of an endpoint of the interval for convex resp. concave potentials.
arxiv