Results 31 to 40 of about 447 (79)

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

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 for a class of p-Laplacian Neumann problems without growth conditions [PDF]

, 2017
For $1p$. We use the shooting method to get existence and multiplicity of non-constant radial solutions. With the same technique, we also detect the oscillatory behavior of the solutions around the constant solution $u\equiv1$.
Boscaggin, Alberto, Colasuonno, Francesca, Noris, Benedetta   +2 more
core   +3 more sources

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

A quasilinear problem with fast growing gradient

, 2012
In this paper we consider the following Dirichlet problem for the $p$-Laplacian in the positive parameters $\lambda$ and $\beta$: [{{array} [c]{rcll}% -\Delta_{p}u & = & \lambda h(x,u)+\beta f(x,u,\nabla u) & \text{in}\Omega u & = & 0 & \text{on}\partial\
Bueno, Hamilton, Ercole, Grey
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

Positive solutions for a nonhomogeneous Schrödinger-Poisson system

Advances in Nonlinear Analysis, 2022
In this article, we consider the following Schrödinger-Poisson system: −Δu+u+k(x)ϕ(x)u=f(x)∣u∣p−1u+g(x),x∈R3,−Δϕ=k(x)u2,x∈R3,\left\{\begin{array}{ll}-\Delta u+u+k\left(x)\phi \left(x)u=f\left(x)| u{| }^{p-1}u+g\left(x),& x\in {{\mathbb{R}}}^{3 ...
Zhang Jing, Niu Rui, Han Xiumei
doaj   +1 more source

Touchdown solutions in general MEMS models

Advances in Nonlinear Analysis, 2023
We study general problems modeling electrostatic microelectromechanical systems devices (Pλ )φ(r,−u′(r))=λ∫0rf(s)g(u(s))ds,r∈(0,1 ...
Clemente Rodrigo, Marcos do Ó João, da Silva Esteban, Shamarova Evelina   +3 more
doaj   +1 more source

Positive multipeak solutions to a zero mass problem in exterior domains

, 2018
We establish the existence of positive multipeak solutions to the nonlinear scalar field equation with zero mass $$-\Delta u = f(u), \qquad u\in D_0^{1,2}(\Omega_R),$$ where $\Omega_R:=\{x \in \mathbb{R}^N:|u|>R\}$ with $R>0$, $N\geq4$, and the ...
Clapp, Mónica, Maia, Liliane A., Pellacci, Benedetta   +2 more
core   +1 more source

Beyond the classical strong maximum principle: Sign-changing forcing term and flat solutions

Advances in Nonlinear Analysis
We show that the classical strong maximum principle, concerning positive supersolutions of linear elliptic equations vanishing on the boundary of the domain can be extended, under suitable conditions, to the case in which the forcing term is sign ...
Díaz Jesús Ildefonso, Hernández Jesús   +1 more
doaj   +1 more source