Results 21 to 30 of about 458 (89)

Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics [PDF]

, 2013
We consider a semilinear elliptic problem [- \Delta u + u = (I_\alpha \ast \abs{u}^p) \abs{u}^{p - 2} u \quad\text{in (\mathbb{R}^N),}] where (I_\alpha) is a Riesz potential and (p>1).
Moroz, Vitaly, Van Schaftingen, Jean
core   +1 more source

(p,Q) systems with critical singular exponential nonlinearities in the Heisenberg group

Open Mathematics, 2020
The paper deals with the existence of solutions for (p,Q)(p,Q) coupled elliptic systems in the Heisenberg group, with critical exponential growth at infinity and singular behavior at the origin.
Pucci Patrizia, Temperini Letizia
doaj   +1 more source

Non-Existence of Positive Stationary Solutions for a Class of Semi-Linear PDEs with Random Coefficients [PDF]

, 2010
We consider a so-called random obstacle model for the motion of a hypersurface through a field of random obstacles, driven by a constant driving field. The resulting semi-linear parabolic PDE with random coefficients does not admit a global nonnegative ...
G. R. Grimmett, J. Xin, L. A. Caffarelli, L. Nirenberg, N. Dirr, N. Dirr, P.-L. Lions, S. Brazovsii   +7 more
core   +3 more sources

Nonzero positive solutions of a multi-parameter elliptic system with functional BCs

, 2017
We prove, by topological methods, new results on the existence of nonzero positive weak solutions for a class of multi-parameter second order elliptic systems subject to functional boundary conditions. The setting is fairly general and covers the case of
Infante, Gennaro
core   +1 more source

Multiple positive solutions to elliptic boundary blow-up problems [PDF]

, 2016
We prove the existence of multiple positive radial solutions to the sign-indefinite elliptic boundary blow-up problem \[ \left\{\begin{array}{ll} \Delta u + \bigl(a^+(\vert x \vert) - \mu a^-(\vert x \vert)\bigr) g(u) = 0, & \; \vert x \vert < 1, \\ u(x)
Aftalion, Alama, Ambrosetti, Bandle, Bandle, Bandle, Barutello, Berestycki, Bieberbach, Bonheure, Boscaggin, Boscaggin, Boscaggin, Boscaggin, Castro, Conley, Dambrosio, Dambrosio, Dambrosio, Ellero, Feltrin, Feltrin, García-Huidobro, García-Melián, García-Melián, Gaudenzi, Gaudenzi, Girão, Gómez-Reñasco, Keller, López-Gómez, López-Gómez, López-Gómez, López-Gómez, Marcus, Mawhin, Medio, Muldowney, Ni, Osserman, Papini, Papini, Papini, Rademacher, Ważewski   +44 more
core   +2 more sources

The Dirichlet problem for fully nonlinear degenerate elliptic equations with a singular nonlinearity

, 2019
We investigate the homogeneous Dirichlet problem in uniformly convex domains for a large class of degenerate elliptic equations with singular zero order term.
Birindelli, Isabeau, Galise, Giulio
core   +1 more source

Symmetric results of a Hénon-type elliptic system with coupled linear part

Open Mathematics, 2022
In this article, we study the elliptic system: −Δu+μ1u=∣x∣αu3+λv,x∈Ω−Δv+μ2v=∣x∣αv3+λu,x∈Ωu,v>0,x∈Ω,u=v=0,x∈∂Ω,\left\{\begin{array}{ll}-\Delta u+{\mu }_{1}u=| x\hspace{-0.25em}{| }^{\alpha }{u}^{3}+\lambda v,& x\in \Omega \\ -\Delta v+{\mu }_{2}v=| x ...
Lou Zhenluo, Li Huimin, Zhang Ping
doaj   +1 more source

Existence and uniqueness of a positive solution to generalized nonlocal thermistor problems with fractional-order derivatives

, 2011
In this work we study a generalized nonlocal thermistor problem with fractional-order Riemann-Liouville derivative. Making use of fixed-point theory, we obtain existence and uniqueness of a positive solution.Comment: Submitted 17-Jul-2011; revised 09-Oct-
Ammi, Moulay Rchid Sidi, Torres, Delfim F. M.   +1 more
core   +1 more source

Existence and non-degeneracy of the normalized spike solutions to the fractional Schrödinger equations

Advances in Nonlinear Analysis
The present study investigates the existence and non-degeneracy of normalized solutions for the following fractional Schrödinger equation: (−Δ)su+V(x)u=aup+μu,x∈RN,u∈Hs(RN){\left(-\Delta )}^{s}u+V\left(x)u=a{u}^{p}+\mu u,\hspace{1.0em}x\in {{\mathbb{R}}}^
Guo Qing, Zhang Yuhang
doaj   +1 more source

Supersolutions to nonautonomous Choquard equations in general domains

Advances in Nonlinear Analysis, 2023
We consider the nonlocal quasilinear elliptic problem: −Δmu(x)=H(x)((Iα*(Qf(u)))(x))βg(u(x))inΩ,-{\Delta }_{m}u\left(x)=H\left(x){(\left({I}_{\alpha }* \left(Qf\left(u)))\left(x))}^{\beta }g\left(u\left(x))\hspace{1.0em}\hspace{0.1em}\text{in}\hspace{0 ...
Aghajani Asadollah, Kinnunen Juha
doaj   +1 more source