Results 31 to 40 of about 521 (76)

Groundstate for the Schrödinger-Poisson-Slater equation involving the Coulomb-Sobolev critical exponent

Advances in Nonlinear Analysis, 2023
In this article, we study the existence of ground state solutions for the Schrödinger-Poisson-Slater type equation with the Coulomb-Sobolev critical growth: −Δu+14π∣x∣∗∣u∣2u=∣u∣u+μ∣u∣p−2u,inR3,-\Delta u+\left(\frac{1}{4\pi | x| }\ast | u{| }^{2}\right)u=|
Lei Chunyu, Lei Jun, Suo Hongmin
doaj   +1 more source

Supercritical Hénon-type equation with a forcing term

Advances in Nonlinear Analysis
This article is concerned with the structure of solutions to the elliptic problem for a Hénon-type equation with a forcing term: −Δu=α(x)up+κμ,inRN,u>0,inRN,(Pκ)\hspace{11.3em}-\Delta u=\alpha \left(x){u}^{p}+\kappa \mu ,\hspace{1.0em}\hspace{0.1em}\text{
Ishige Kazuhiro, Katayama Sho
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The existence and multiplicity of L 2-normalized solutions to nonlinear Schrödinger equations with variable coefficients

Advanced Nonlinear Studies
The existence of L 2–normalized solutions is studied for the equation −Δu+μu=f(x,u)  inRN,∫RNu2dx=m. $-{\Delta}u+\mu u=f\left(x,u\right)\quad \quad \text{in} {\mathbf{R}}^{N},\quad {\int }_{{\mathbf{R}}^{N}}{u}^{2} \mathrm{d}x=m.$ Here m > 0 and f(x, s)
Ikoma Norihisa, Yamanobe Mizuki
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Conformally covariant parameterizations for relativistic initial data

, 2016
We revisit the Lichnerowicz-York method, and an alternative method of York, in order to obtain some conformally covariant systems.
Delay, Erwann
core   +2 more sources

Uniqueness and nondegeneracy of ground states for −Δu+u=(Iα⋆u2)u-\Delta u+u=\left({{\rm{I}}}_{\alpha }\star {u}^{2})u in R3{{\mathbb{R}}}^{3} when α\alpha is close to 2

Advances in Nonlinear Analysis
In this article, we study the following Choquard equation: −Δu+u=(Iα⋆u2)u,x∈R3,-\Delta u+u=\left({{\rm{I}}}_{\alpha }\star {u}^{2})u,\hspace{1.0em}x\in {{\mathbb{R}}}^{3}, where Iα{{\rm{I}}}_{\alpha } is the Riesz potential and α\alpha is sufficiently ...
Luo Huxiao, Zhang Dingliang, Xu Yating
doaj   +1 more source

Reaction-diffusion problems on time-dependent Riemannian manifolds: stability of periodic solutions

, 2017
We investigate the stability of time-periodic solutions of semilinear parabolic problems with Neumann boundary conditions. Such problems are posed on compact submanifolds evolving periodically in time.
Bandle, Catherine, Monticelli, Dario Daniele, Punzo, Fabio   +2 more
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Weak and stationary solutions to a Cahn–Hilliard–Brinkman model with singular potentials and source terms

Advances in Nonlinear Analysis, 2020
We study a phase field model proposed recently in the context of tumour growth. The model couples a Cahn–Hilliard–Brinkman (CHB) system with an elliptic reaction-diffusion equation for a nutrient.
Ebenbeck Matthias, Lam Kei Fong
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Lane-Emden equations perturbed by nonhomogeneous potential in the super critical case

Advances in Nonlinear Analysis, 2021
Our purpose of this paper is to study positive solutions of Lane-Emden ...
Ma Yong, Wang Ying, Ledesma César T.
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Existence, uniqueness, localization and minimization property of positive solutions for non-local problems involving discontinuous Kirchhoff functions

Advances in Nonlinear Analysis
Let Ω⊂Rn\Omega \subset {{\bf{R}}}^{n} be a smooth bounded domain. In this article, we prove a result of which the following is a by-product: Let q∈]0,1[q\in ]0,1{[}, α∈L∞(Ω)\alpha \in {L}^{\infty }\left(\Omega ), with α>0\alpha \gt 0, and k∈Nk\in {\bf{N}}
Ricceri Biagio
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Infinitely many solutions for cubic nonlinear Schrödinger equations in dimension four

Advances in Nonlinear Analysis, 2017
We extend Chen, Wei and Yan’s constructions of families of solutions with unbounded energies [5] to the case of cubic nonlinear Schrödinger equations in the optimal dimension four.
Vétois Jérôme, Wang Shaodong
doaj   +1 more source