Results 21 to 30 of about 59 (53)

Existence and Asymptotic Profile of Nodal Solutions to Supercritical Problems

open access: yesAdvanced Nonlinear Studies, 2017
We establish the existence of nodal solutions to the supercritical ...
Clapp Mónica, Pacella Filomena
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Groundstate for the Schrödinger-Poisson-Slater equation involving the Coulomb-Sobolev critical exponent

open access: yesAdvances 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
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Fast and Slow Decaying Solutions of Lane–Emden Equations Involving Nonhomogeneous Potential

open access: yesAdvanced Nonlinear Studies, 2020
Our purpose in this paper is to study positive solutions of the Lane–Emden ...
Chen Huyuan, Huang Xia, Zhou Feng
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Periodic Solutions of Non-autonomous Allen–Cahn Equations Involving Fractional Laplacian

open access: yesAdvanced Nonlinear Studies, 2020
We consider periodic solutions of the following problem associated with the fractional Laplacian: (-∂x⁢x)s⁢u⁢(x)+∂u⁡F⁢(x,u⁢(x))=0{(-\partial_{xx})^{s}u(x)+\partial_{u}F(x,u(x))=0} in ℝ{\mathbb{R}}.
Feng Zhenping, Du Zhuoran
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Supercritical Hénon-type equation with a forcing term

open access: yesAdvances 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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Infinitely many solutions for cubic nonlinear Schrödinger equations in dimension four

open access: yesAdvances 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
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The existence and multiplicity of L 2-normalized solutions to nonlinear Schrödinger equations with variable coefficients

open access: yesAdvanced 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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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

open access: yesAdvances 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
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Lane-Emden equations perturbed by nonhomogeneous potential in the super critical case

open access: yesAdvances 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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Weak and stationary solutions to a Cahn–Hilliard–Brinkman model with singular potentials and source terms

open access: yesAdvances 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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