Results 31 to 40 of about 86 (56)

Ground state solutions of nonlinear Schrödinger equations involving the fractional p-Laplacian and potential wells

Open Mathematics, 2022
The purpose of this paper is to investigate the ground state solutions for the following nonlinear Schrödinger equations involving the fractional p-Laplacian (−Δ)psu(x)+λV(x)u(x)p−1=u(x)q−1,u(x)≥0,x∈RN,{\left(-\Delta )}_{p}^{s}u\left(x)+\lambda V\left(x ...
Chen Yongpeng, Niu Miaomiao
doaj   +1 more source

Multiplicity of positive solutions for a concave-convex fractional elliptic system with critical growth

Demonstratio Mathematica
In this paper, the following fractional elliptic system involving critical growth terms is considered(−Δ)su=αα+β|u|α−2u|v|β+λ|u|q−2u|x|γ, inΩ,(−Δ)sv=βα+β|u|α|v|β−2v+μ|v|q−2v|x|γ, inΩ,u=v=0, on∂Ω, $$\begin{cases}{\left(-{\Delta}\right)}^{s}u=\frac{\alpha }
Kang Qiao, Liao Jia-Feng
doaj   +1 more source

Existence and Concentration of Solutions for Choquard Equations with Steep Potential Well and Doubly Critical Exponents

Advanced Nonlinear Studies, 2021
In this paper, we investigate the non-autonomous Choquard ...
Li Yong-Yong, Li Gui-Dong, Tang Chun-Lei
doaj   +1 more source

Existence results for nonhomogeneous Choquard equation involving p-biharmonic operator and critical growth

Demonstratio Mathematica
In this article, we are interested in the existence of nontrivial solutions for the following nonhomogeneous Choquard equation involving the pp-biharmonic operator: M∫Ω∣Δu∣pdxΔp2u−Δpu=λ(∣x∣−μ⁎∣u∣q)∣u∣q−2u+∣u∣p*−2u+f,inΩ,u=Δu=0,on∂Ω,\left\{\begin{array}{l}
Hai Quan, Zhang Jing
doaj   +1 more source

Existence and Convergence of Solutions to Fractional Pure Critical Exponent Problems

Advanced Nonlinear Studies, 2021
We study existence and convergence properties of least-energy symmetric solutions (l.e.s.s.) to the pure critical exponent ...
Hernández-Santamaría Víctor, Saldaña Alberto   +1 more
doaj   +1 more source

Multiple positive solutions for a class of concave-convex Schrödinger-Poisson-Slater equations with critical exponent

Advances in Nonlinear Analysis
In this article, we consider the multiplicity of positive solutions for a static Schrödinger-Poisson-Slater equation of the type −Δu+u2∗1∣4πx∣u=μf(x)∣u∣p−2u+g(x)∣u∣4uinR3,-\Delta u+\left({u}^{2}\ast \frac{1}{| 4\pi x| }\right)u=\mu f\left(x){| u| }^{p-2 ...
Zheng Tian-Tian, Lei Chun-Yu, Liao Jia-Feng   +2 more
doaj   +1 more source

Existence and concentration behavior of positive solutions to Schrödinger-Poisson-Slater equations

Advances in Nonlinear Analysis, 2023
This article is directed to the study of the following Schrödinger-Poisson-Slater type equation: −ε2Δu+V(x)u+ε−α(Iα∗∣u∣2)u=λ∣u∣p−1uinRN,-{\varepsilon }^{2}\Delta u+V\left(x)u+{\varepsilon }^{-\alpha }\left({I}_{\alpha }\ast | u{| }^{2})u=\lambda | u{| }^{
Li Yiqing, Zhang Binlin, Han Xiumei
doaj   +1 more source

Existence and Asymptotic Behavior of Positive Solutions for a Class of Quasilinear Schrödinger Equations

Advanced Nonlinear Studies, 2018
In this paper, we study the quasilinear Schrödinger equation -Δ⁢u+V⁢(x)⁢u-γ2⁢(Δ⁢u2)⁢u=|u|p-2⁢u{-\Delta u+V(x)u-\frac{\gamma}{2}(\Delta u^{2})u=|u|^{p-2}u}, x∈ℝN{x\in\mathbb{R}^{N}}, where V⁢(x):ℝN→ℝ{V(x):\mathbb{R}^{N}\to\mathbb{R}} is a given potential,
Wang Youjun, Shen Yaotian
doaj   +1 more source

Blow-Up Results for Higher-Order Evolution Differential Inequalities in Exterior Domains

Advanced Nonlinear Studies, 2019
We consider a higher-order evolution differential inequality in an exterior domain of ℝN{\mathbb{R}^{N}}, N≥3{N\geq 3}, with Dirichlet and Neumann boundary conditions.
Jleli Mohamed, Kirane Mokhtar, Samet Bessem   +2 more
doaj   +1 more source

Infinitely many solutions for Hamiltonian system with critical growth

Advances in Nonlinear Analysis
In this article, we consider the following elliptic system of Hamiltonian-type on a bounded domain:−Δu=K1(∣y∣)∣v∣p−1v,inB1(0),−Δv=K2(∣y∣)∣u∣q−1u,inB1(0),u=v=0on∂B1(0),\left\{\begin{array}{ll}-\Delta u={K}_{1}\left(| y| ){| v| }^{p-1}v,\hspace{1.0em ...
Guo Yuxia, Hu Yichen
doaj   +1 more source