Existence of Ground States of Fractional Schrödinger Equations
Advanced Nonlinear Studies, 2021 We consider ground states of the nonlinear fractional Schrödinger equation with ...
Ma Li, Li Zhenxiong
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On a Class of Reaction-Diffusion Equations with Aggregation
Advanced Nonlinear Studies, 2021 In this paper, global-in-time existence and blow-up results are shown for a reaction-diffusion equation appearing in the theory of aggregation phenomena (including chemotaxis).
Chen Li +2 more
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On singular solutions of Lane-Emden equation on the Heisenberg group
Advanced Nonlinear Studies, 2023 By applying the gluing method, we construct infinitely many axial symmetric singular positive solutions to the Lane-Emden equation: ΔHu+up=0,inHn\{0}{\Delta }_{{\mathbb{H}}}u+{u}^{p}=0\left,\hspace{1.0em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0 ...
Wei Juncheng, Wu Ke
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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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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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On the solutions of a singular elliptic equation concentrating on a circle
Advances in Nonlinear Analysis, 2014 Let A={x∈ℝ2N+2 ...
Manna Bhakti B. +1 more
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Positivity of solutions to the Cauchy problem for linear and semilinear biharmonic heat equations
Advances in Nonlinear Analysis, 2020 This paper is concerned with the positivity of solutions to the Cauchy problem for linear and nonlinear parabolic equations with the biharmonic operator as fourth order elliptic principal part. Generally, Cauchy problems for parabolic equations of fourth
Grunau Hans-Christoph +2 more
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A class of semipositone p-Laplacian problems with a critical growth reaction term
Advances in Nonlinear Analysis, 2019 We prove the existence of ground state positive solutions for a class of semipositone p-Laplacian problems with a critical growth reaction term. The proofs are established by obtaining crucial uniform C1,α a priori estimates and by concentration ...
Perera Kanishka +2 more
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Torsion and ground state maxima: close but not the same
, 2015 Could the location of the maximum point for a positive solution of a semilinear Poisson equation on a convex domain be independent of the form of the nonlinearity? Cima and Derrick found certain evidence for this surprising conjecture.
Benson, Brian A. +3 more
core
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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