Complete classification of ground state solutions with different Morse index for critical fractional Laplacian system
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DOI: 10.1002/mma.6862
Abstract: In this paper, we first obtain the existence of positive ground state solutions for the following critical fractional Laplacian system: (−Δ)su=μ1|u|2s∗−2u+αγ2s∗|u|α−2u|v|βinℝn,(−Δ)sv=μ2|v|2s∗−2v+βγ2s∗|u|α|v|β−2vinℝn, then we give a complete classification of positive ground state solutions with different Morse… read more here.
Keywords: ground state; morse index; state solutions; ground ... See more keywords
Ground State Solutions for a Quasilinear Schrödinger Equation
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DOI: 10.1007/s00009-016-0816-3
Abstract: In this paper, we study the following quasilinear Schrödinger equation of the form $$\begin{aligned} -\Delta u+V(x)u-\Delta (u^{2})u= g(x,u),~~~ x\in \mathbb {R}^N \end{aligned}$$-Δu+V(x)u-Δ(u2)u=g(x,u),x∈RNwhere V and g are 1-periodic in $$x_{1},\ldots ,x_{N}$$x1,…,xN, and g is a superlinear… read more here.
Keywords: dinger equation; state solutions; quasilinear schr; ground state ... See more keywords
On the Existence of Ground State Solutions for Fractional Schrödinger–Poisson Systems with General Potentials and Super-quadratic Nonlinearity
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DOI: 10.1007/s00009-018-1179-8
Abstract: In this article, we are concerned with the following fractional Schrödinger–Poisson system: $$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^{s}u+V(x)u+\phi u=f(u)&{} \quad \hbox {in}~\mathbb {R}^{3},\\ (-\Delta )^{t}\phi =u^2&{} \quad \hbox {in}~\mathbb {R}^{3},\\ \end{array} \right. \end{aligned}$$(-Δ)su+V(x)u+ϕu=f(u)inR3,(-Δ)tϕ=u2inR3,where $$03$$2s+2t>3, and $$f\in… read more here.
Keywords: dinger poisson; fractional schr; state solutions; ground state ... See more keywords
Existence of Ground State Solutions for Fractional Schrödinger–Poisson Systems with Doubly Critical Growth
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DOI: 10.1007/s00009-020-01660-x
Abstract: This paper considers a class of fractional Schrodinger–Poisson type systems with doubly critical growth $$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^su+V(x)u-\phi |u|^{2^*_s-3}u=K(x)|u|^{2^*_s-2}u,&{} \text{ in } {\mathbb {R}}^3,\\ (-\Delta )^s\phi =|u|^{2^*_s-1},&{} \text{ in } {\mathbb {R}}^3, \end{array}\right. \end{aligned}$$… read more here.
Keywords: ground state; systems doubly; doubly critical; state solutions ... See more keywords
Nehari-Type Ground State Solutions for Superlinear Elliptic Equations with Variable Exponent in $${\mathbb {R}}^N$$
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DOI: 10.1007/s00009-021-01704-w
Abstract: We deal with the existence of Nehari-type ground state solutions for the superlinear p(x)-Laplacian equation $$\begin{aligned} -\triangle _{p(x)} u+V(x)|u|^{p(x)-2}u= f(x,u),\; x\in {\mathbb {R}}^N,\;u\in W^{1,p(x)}({\mathbb {R}}^N). \end{aligned}$$ Under a weaker Nehari condition, we establish some existence… read more here.
Keywords: state solutions; ground state; type ground; nehari type ... See more keywords
Stable cationic coordination polymers of the Cu(II)-vitamin B6 type: Structural analysis, application abilities and physicochemical properties in the solid state and solutions
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DOI: 10.1016/j.dyepig.2016.08.055
Abstract: Abstract The stability of two cationic coordination polymers, {[Cu(NO3)(pm)2]}nNO3·H2O and {[Cu(Cl)(pn)2]}nNO3 (pm and pn denote pyridoxamine and pyridoxine, respectively), have been investigated in the solid state and solutions. The characterization of the solid precipitates has… read more here.
Keywords: solid state; coordination; cationic coordination; state solutions ... See more keywords
Nonexistence of nonconstant steady-state solutions in a triangular cross-diffusion model
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DOI: 10.1016/j.jde.2017.01.017
Abstract: Abstract In this paper we study the Shigesada–Kawasaki–Teramoto model for two competing species with triangular cross-diffusion. We determine explicit parameter ranges within which the model exclusively possesses constant steady state solutions. read more here.
Keywords: model; state solutions; steady state; triangular cross ... See more keywords
Qualitative analysis on positive steady-state solutions for an autocatalysis model with high order
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DOI: 10.1016/j.nonrwa.2017.11.010
Abstract: Abstract This paper is concerned with an autocatalysis model with high order under Neumann boundary conditions. Firstly, the stability of the equilibrium is discussed and the effect of diffusion coefficients on Turing instability is described.… read more here.
Keywords: model high; positive steady; high order; steady state ... See more keywords
Existence of ground state solutions to Hamiltonian elliptic system with potentials
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DOI: 10.1016/s0252-9602(18)30859-2
Abstract: Abstract In this paper, we investigate nonlinear Hamiltonian elliptic system { ( - Δ ) u = b → ( x ) ⋅ ∇ u + ( V ( x ) + τ ) u… read more here.
Keywords: hamiltonian elliptic; elliptic system; state solutions; ground state ... See more keywords
Concentrating ground state solutions for quasilinear Schrödinger equations with steep potential well
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DOI: 10.1080/00036811.2019.1707814
Abstract: We are concerned with the following quasilinear Schrödinger equations (1) where , are parameters, V and f are nonnegative continuous functions, is a positive bounded function. By using variational methods, we study the existence of… read more here.
Keywords: dinger equations; state solutions; quasilinear schr; ground state ... See more keywords
Sign-changing ground state solutions for discrete nonlinear Schrödinger equations
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DOI: 10.1080/10236198.2018.1563601
Abstract: ABSTRACT In this paper, we study the existence of least energy sign-changing solutions and ground state solutions for the discrete nonlinear Schrödinger equation where is a sequence of positive numbers, is a constant. By using… read more here.
Keywords: sign changing; ground state; state solutions; solutions discrete ... See more keywords