Results 41 to 50 of about 86 (75)

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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Positive solutions for the fractional Schrödinger equations with logarithmic and critical non‐linearities

Transactions of the London Mathematical Society, 2021
In this paper, we study a class of fractional Schrödinger equations involving logarithmic and critical non‐linearities on an unbounded domain, and show that such an equation with positive or sign‐changing weight potentials admits at least one positive ...
Haining Fan, Zhaosheng Feng, Xingjie Yan
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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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Ground state solutions and multiple positive solutions for nonhomogeneous Kirchhoff equation with Berestycki-Lions type conditions

Demonstratio Mathematica
This article is concerned with the following Kirchhoff equation: −a+b∫R3∣∇u∣2dxΔu=g(u)+h(x)inR3,-\left(a+b\mathop{\int }\limits_{{{\mathbb{R}}}^{3}}{| \nabla u| }^{2}{\rm{d}}x\right)\Delta u=g\left(u)+h\left(x)\hspace{1em}{\rm{in}}\hspace{0.33em ...
Huang Lanxin, Su Jiabao
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Existence of Ground States of Fractional Schrödinger Equations

Advanced Nonlinear Studies, 2021
We consider ground states of the nonlinear fractional Schrödinger equation with ...
Ma Li, Li Zhenxiong
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Concentration phenomena for a fractional relativistic Schrödinger equation with critical growth

Advances in Nonlinear Analysis
In this paper, we are concerned with the following fractional relativistic Schrödinger equation with critical growth: (−Δ+m2)su+V(εx)u=f(u)+u2s*−1inRN,u∈Hs(RN),u>0inRN,\left\{\begin{array}{ll}{\left(-\Delta +{m}^{2})}^{s}u+V\left(\varepsilon x)u=f\left(u)
Ambrosio Vincenzo
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A uniqueness result for the fractional Schrödinger-Poisson system with strong singularity

Open Mathematics
This article considers existence of solution for a class of fractional Schrödinger-Poisson system. By using the Nehari method and the variational method, we obtain a uniqueness result for positive solutions.
Wang Li, Chen Renhua, Zhong Qiaocheng, Wang Jun, Li Fang   +4 more
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On the solutions of a singular elliptic equation concentrating on a circle

Advances in Nonlinear Analysis, 2014
Let A={x∈ℝ2N+2 ...
Manna Bhakti B., Srikanth P. Chakravarthy   +1 more
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A class of semipositone p-Laplacian problems with a critical growth reaction term

Advances in Nonlinear Analysis, 2019
We prove the existence of ground state positive solutions for a class of semipositone p-Laplacian problems with a critical growth reaction term. The proofs are established by obtaining crucial uniform C1,α a priori estimates and by concentration ...
Perera Kanishka, Shivaji Ratnasingham, Sim Inbo   +2 more
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Positivity of solutions to the Cauchy problem for linear and semilinear biharmonic heat equations

Advances in Nonlinear Analysis, 2020
This paper is concerned with the positivity of solutions to the Cauchy problem for linear and nonlinear parabolic equations with the biharmonic operator as fourth order elliptic principal part. Generally, Cauchy problems for parabolic equations of fourth
Grunau Hans-Christoph, Miyake Nobuhito, Okabe Shinya   +2 more
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