Results 91 to 100 of about 1,675,583 (134)

On the existence of a priori bounds for positive solutions of elliptic problems, I

Revista Integración, 2019
This paper gives a survey over the existence of uniform L∞ a priori bounds for positive solutions of subcritical elliptic equations (P)p     -\Delta_p u =f(u),  in  \Omega,    u = 0, on \partial\Omega widening the known ranges of subcritical ...
Rosa Pardo
doaj  

Solutions to the Prescribed Positive Q-Curvature Equation with Power-Law Singular Terms in ${\mathbb{R}}^4$

Axioms
This paper investigates the solution theory of a class of prescribed positive Q-curvature equations with power-law singularity at the origin and polynomial growth at infinity in the four-dimensional Euclidean space. We focus on the equation involving the
Dejun Tai, Zixin Ren, Yumei Xing
doaj   +1 more source

Infinitely many free or prescribed mass solutions for fractional Hartree equations and Pohozaev identities

Advanced Nonlinear Studies
In this paper we study the following nonlinear fractional Hartree (or Choquard-Pekar) equation (−Δ)su+μu=(Iα*F(u))F′(u) inRN, ${\left(-{\Delta}\right)}^{s}u+\mu u=\left({I}_{\alpha }{\ast}F\left(u\right)\right){F}^{\prime }\left(u\right)\quad \text{in} {\
Cingolani Silvia, Gallo Marco, Tanaka Kazunaga   +2 more
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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

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

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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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
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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
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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