Fractional Schrödinger-Poisson systems with a general subcritical or critical nonlinearity [PDF]
arXiv, 2015 We consider a fractional Schr\"{o}dinger-Poisson system with a general nonlinearity in subcritical and critical case. The Ambrosetti-Rabinowitz condition is not required. By using a perturbation approach, we prove the existence of positive solutions. Moreover, we study the asymptotics of solutions for a vanishing parameter.
arxiv
Some remarks on the structure of finite Morse index solutions to the Allen-Cahn equation in $\mathbb{R}^2$ [PDF]
arXiv, 2015 For a solution of the Allen-Cahn equation in $\mathbb{R}^2$, under the natural linear growth energy bound, we show that the blowing down limit is unique. Furthermore, if the solution has finite Morse index, the blowing down limit satisfies the multiplicity one property.
arxiv
Global Dynamics of Generalized Logistic Equations
Advanced Nonlinear Studies, 2018 We consider a parameter dependent parabolic logistic population model with diffusion and degenerate logistic term allowing for refuges for the population.
Daners Daniel, López-Gómez Julián
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Solution of the fractional Allen-Cahn equation which are invariant under screw motion [PDF]
arXiv, 2015 We establish existence and non-existence results for entire solutions to the fractional Allen-Cahn equation in $\mathbb R^3$, which vanish on helicoids and are invariant under screw-motion. In addition, we prove that helicoids are surfaces with vanishing nonlocal mean curvature.
arxiv
Loop Type Subcontinua of Positive Solutions for Indefinite Concave-Convex Problems
Advanced Nonlinear Studies, 2019 We establish the existence of loop type subcontinua of nonnegative solutions for a class of concave-convex type elliptic equations with indefinite weights, under Dirichlet and Neumann boundary conditions.
Kaufmann Uriel +2 more
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Regularity of solutions in semilinear elliptic theory [PDF]
arXiv, 2016 We study the semilinear Poisson equation \begin{equation} \label{pro} \Delta u = f(x, u) \hskip .2 in \text{in} \hskip .2 in B_1. \end{equation} Our main results provide conditions on $f$ which ensure that weak solutions of this equation belong to $C^{1,1}(B_{1/2})$. In some configurations, the conditions are sharp.
arxiv
Diffusive logistic equations with harvesting and heterogeneity under strong growth rate
Advances in Nonlinear Analysis, 2017 We consider the ...
Shabani Rokn-e-vafa Saeed +1 more
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Nonlinear Schrödinger equation with bounded magnetic field [PDF]
arXiv, 2019 The paper studies existence of solutions for the nonlinear Schr\"odinger equation with a general bounded external magnetic field. In particular, no lattice periodicity of the magnetic field or presence of external electric field is required. Solutions are obtained by means of a general structural statement about bounded sequences in the magnetic ...
arxiv
On the moving plane method for boundary blow-up solutions to semilinear elliptic equations
Advances in Nonlinear Analysis, 2018 We consider weak solutions to -Δu=f(u){-\Delta u=f(u)} on Ω1∖Ω0{\Omega_{1}\setminus\Omega_{0}}, with u=c≥0{u=c\geq 0} in ∂Ω1{\partial\Omega_{1}} and u=+∞{u=+\infty} on ∂Ω0{\partial\Omega_{0}}, and we prove monotonicity properties of the solutions via
Canino Annamaria +2 more
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Choquard-type equations with Hardy–Littlewood–Sobolev upper-critical growth
Advances in Nonlinear Analysis, 2018 We are concerned with the existence of ground states and qualitative properties of solutions for a class of nonlocal Schrödinger equations. We consider the case in which the nonlinearity exhibits critical growth in the sense of the Hardy–Littlewood ...
Cassani Daniele, Zhang Jianjun
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