Results 1 to 10 of about 113 (83)
Fourth order elliptic system with dirichlet boundary condition
Journal of Inequalities and Applications, 2011 We investigate the multiplicity of the solutions of the fourth order elliptic system with Dirichlet boundary condition. We get two theorems. One theorem is that the fourth order elliptic system has at least two nontrivial solutions when λ k < c &
Choi Q-Heung, Jung Tacksun
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A Caccioppoli-type estimate for very weak solutions to obstacle problems with weight
Journal of Inequalities and Applications, 2011 This paper gives a Caccioppoli-type estimate for very weak solutions to obstacle problems of the A -harmonic equation div A ( x , ∇ u ) = 0 with | A ( x , ξ ) | ≈ w ( x ) | ξ | p - 1 , where 1 < p < ...
Hongya Gao, Jinjing Qiao
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Multiple nodal solutions of the Kirchhoff-type problem with a cubic term
Advances in Nonlinear Analysis, 2022 In this article, we are interested in the following Kirchhoff-type problem (0.1)−a+b∫RN∣∇u∣2dxΔu+V(∣x∣)u=∣u∣2uinRN,u∈H1(RN),\left\{\begin{array}{l}-\left(a+b\mathop{\displaystyle \int }\limits_{{{\mathbb{R}}}^{N}}| \nabla u\hspace{-0.25em}{| }^{2}{\rm{d}}
Wang Tao, Yang Yanling, Guo Hui
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Existence and asymptotic behavior of solitary waves for a weakly coupled Schrödinger system
Advanced Nonlinear Studies, 2022 This paper deals with the following weakly coupled nonlinear Schrödinger system −Δu1+a1(x)u1=∣u1∣2p−2u1+b∣u1∣p−2∣u2∣pu1,x∈RN,−Δu2+a2(x)u2=∣u2∣2p−2u2+b∣u2∣p−2∣u1∣pu2,x∈RN,\left\{\begin{array}{ll}-\Delta {u}_{1}+{a}_{1}\left(x){u}_{1}=| {u}_{1}{| }^{2p-2 ...
An Xiaoming, Yang Jing
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Ground states of Schrödinger systems with the Chern-Simons gauge fields
Advanced Nonlinear Studies, 2023 We are concerned with the following coupled nonlinear Schrödinger system: −Δu+u+∫∣x∣∞h(s)su2(s)ds+h2(∣x∣)∣x∣2u=∣u∣2p−2u+b∣v∣p∣u∣p−2u,x∈R2,−Δv+ωv+∫∣x∣∞g(s)sv2(s)ds+g2(∣x∣)∣x∣2v=∣v∣2p−2v+b∣u∣p∣v∣p−2v,x∈R2,\left\{\begin{array}{l}-\Delta u+u+\left(\underset{|
Jiang Yahui +4 more
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Normalized solutions for a class of scalar field equations involving mixed fractional Laplacians
Advanced Nonlinear Studies, 2022 The purpose of this article is to establish sharp conditions for the existence of normalized solutions to a class of scalar field equations involving mixed fractional Laplacians with different orders.
Luo Tingjian, Hajaiej Hichem
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Relativistic Chern–Simons–Higgs vortex equations [PDF]
, 2015 An existence theorem is established for the solutions to the non-Abelian relativistic Chern-Simons-Higgs vortex equations over a doubly periodic domain when the gauge group G assumes the most general and important prototype form, G = SU(N).
Xiaosen Han, Yisong Yang
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Existence of positive ground states for some nonlinear Schrödinger systems
Boundary Value Problems, 2013 We prove the existence of positive ground states for the nonlinear Schrödinger system {−Δu+(1+a(x))u=Fu(u,v)+λv,−Δv+(1+b(x))v=Fv(u,v)+λu, where a, b are periodic or asymptotically periodic and F satisfies some superlinear conditions in (u,v). The proof
Hui Zhang, Junxiang Xu, Fubao Zhang
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Multiple solutions for p-Laplacian systems with critical homogeneous nonlinearity
Boundary Value Problems, 2012 In this article, we deal with existence and multiplicity of solutions to the p-Laplacian system of the type -Δpu=1p*∂F(x,u,v)∂u+λuq-2u,x∈Ω,-Δpv=1p*∂F(x,u,v)∂v+δvq-2v,x∈Ω,u=v=0,x∈∂Ω, where Ω ⊂ ℝNis a bounded domain with ...
Dengfeng Lü
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The Weak Galerkin Method for Elliptic Eigenvalue Problems
Communications in Computational Physics, 2019 This article is devoted to studying the application of the weak Galerkin (WG) finite element method to the elliptic eigenvalue problem with an emphasis on obtaining lower bounds.
Q. Zhai
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