Results 61 to 70 of about 95 (88)

Uniqueness of Single Peak Solutions for a Kirchhoff Equation

Mathematics
We deal with the following singular perturbation Kirchhoff equation: −ϵ2a+ϵb∫R3|∇u|2dyΔu+Q(y)u=|u|p−1u,u∈H1(R3), where constants a,b,ϵ>0 and ...
Junhao Lv, Shichao Yi, Bo Sun
doaj   +1 more source

Non-negative and positive solutions for some indefinite sublinear elliptic problems

Boundary Value Problems
We study the existence of non-negative and positive solutions to the indefinite sublinear elliptic problem − Δ u = λ u + m ( x ) | u | α − 1 u $\ -\Delta u=\lambda u+m(x)\left \vert u\right \vert ^{\alpha -1}u$ in Ω, u = 0 $u=0$ on ∂Ω, where Ω is a ...
J. I. Díaz, J. Hernández, Y. Ilyasov
doaj   +1 more source

Existence and Stability in Nonlocal Schrödinger–Poisson–Slater Equations

Fractal and Fractional
In this paper, we study a class of nonlocal Schrödinger–Poisson–Slater equations: −Δu+u+λIα∗|u|q|u|q−2u=|u|p−2u, where q,p>1, λ>0, and Iα is the Riesz potential.
Fangyuan Dong, Zhaoyang Wang, Hui Liu, Limei Cao   +3 more
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Global existence and energy decay rates for a Kirchhoff-type wave equation with nonlinear dissipation. [PDF]

ScientificWorldJournal, 2014
Kim D, Kim D, Hong KS, Jung IH.
europepmc   +1 more source

Normalized Solutions and Critical Growth in Fractional Nonlinear Schrödinger Equations with Potential

Fractal and Fractional
We investigate the existence of positive normalized (mass-constrained) solutions for the fractional nonlinear Schrödinger equation (−Δ)sv+V(x)v=λv+μ|v|p−2v+|v|2s*−2vinRN,∥v∥22=b2, where N>2s, s∈(0,1), μ>0, p∈(2,2s*), and 2s*=2NN−2s. Here, λ∈R denotes the
Jie Xu, Qiongfen Zhang, Xingwen Chen
doaj   +1 more source

Critical Fractional Problems with Weights: Existence, Minimization, and Pohozaev Obstructions

Mathematics
Recently, a great amount of attention has been focused on the study of fractional and nonlocal operators of the elliptic type both for pure mathematical research and in view of concrete real-world applications.
Sana Benhafsia, Rejeb Hadiji
doaj   +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