Existence and multiplicity of positive solutions for elliptic systems

1997 ◽  
Vol 29 (9) ◽  
pp. 1051-1060 ◽  
Author(s):  
D.R. Dunninger ◽  
Haiyan Wang
Keyword(s):  
Positive Solutions ◽  
Elliptic Systems ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions

Multiple positive solutions of elliptic systems in exterior domains

2018 ◽  
Vol 20 (06) ◽  
pp. 1750063 ◽  
Author(s):  
Haidong Liu ◽  
Zhaoli Liu
Keyword(s):  
Positive Solutions ◽  
Exterior Domain ◽  
Elliptic Systems ◽  
Continuous Functions ◽  
Multiple Positive Solutions ◽  
Exterior Domains ◽  
Existence And Multiplicity ◽  
Large Ball ◽  
Multiplicity Of Positive Solutions ◽  
Positive Functions

In this paper, existence and multiplicity of positive solutions of the elliptic system [Formula: see text] is proved, where [Formula: see text] is an exterior domain in [Formula: see text] such that [Formula: see text] is far away from the origin and contains a sufficiently large ball, [Formula: see text], and the coefficients [Formula: see text] are continuous functions on [Formula: see text] which tend to positive constants at infinity. We do not assume [Formula: see text] to be positive functions.

Multiplicity of Positive Solutions for Critical Singular Elliptic Systems With Concave-Convex Nonlinearities

2009 ◽  
Vol 9 (2) ◽  
Author(s):  
Tsing-San Hsu
Keyword(s):  
Variational Methods ◽  
Elliptic System ◽  
Positive Solutions ◽  
Elliptic Systems ◽  
Critical Growth ◽  
Bounded Domains ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions

AbstractIn this paper, we consider a singular elliptic system with both concave-convex nonlinearities and critical growth terms in bounded domains. The existence and multiplicity results of positive solutions are obtained by variational methods.

scholarly journals Positive Solutions for a Class of Nonlinear Singular Fractional Differential Systems with Riemann–Stieltjes Coupled Integral Boundary Value Conditions

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 107
Author(s):  
Daliang Zhao ◽  
Juan Mao
Keyword(s):  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Main Tool ◽  
Integral Boundary ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Existence And Multiplicity ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions

In this paper, sufficient conditions ensuring existence and multiplicity of positive solutions for a class of nonlinear singular fractional differential systems are derived with Riemann–Stieltjes coupled integral boundary value conditions in Banach Spaces. Nonlinear functions f(t,u,v) and g(t,u,v) in the considered systems are allowed to be singular at every variable. The boundary conditions here are coupled forms with Riemann–Stieltjes integrals. In order to overcome the difficulties arising from the singularity, a suitable cone is constructed through the properties of Green’s functions associated with the systems. The main tool used in the present paper is the fixed point theorem on cone. Lastly, an example is offered to show the effectiveness of our obtained new results.

Existence and multiplicity of positive solutions for the nonlinear Schrödinger–Poisson equations

2013 ◽  
Vol 143 (4) ◽  
pp. 745-764 ◽  
Author(s):  
Ching-yu Chen ◽  
Yueh-cheng Kuo ◽  
Tsung-fang Wu
Keyword(s):  
Positive Solutions ◽  
Nonlinear Schrödinger ◽  
Poisson Equations ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions ◽  
Image Position

We study the existence and multiplicity of positive solutions for the following nonlinear Schrödinger–Poisson equations: where 2 < p ≤ 3 or 4 ≤ p < 6, λ > 0 and Q ∈ C(ℝ3). We show that the number of positive solutions is dependent on the profile of Q(x).

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