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).

Existence and Multiplicity of Positive Solutions for Singular Semipositone p-Laplacian Equations

2006 ◽  
Vol 58 (3) ◽  
pp. 449-475 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Daomin Cao ◽  
Haishen Lü ◽  
Donal O'Regan
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Solution Method ◽  
Degree Theory ◽  
Lower Solution ◽  
Existence And Multiplicity ◽  
Lower Solution Method ◽  
Multiplicity Of Positive Solutions ◽  
Image Position ◽  
Laplacian Equations

AbstractPositive solutions are obtained for the boundary value problemHere f (t, u) ≥ –M, (M is a positive constant) for (t, u) ∈ [0, 1]×(0, ∞). We will show the existence of two positive solutions by using degree theory together with the upper–lower solution method.

Non-homogeneous elliptic equations in exterior domains

2006 ◽  
Vol 136 (1) ◽  
pp. 139-147 ◽  
Author(s):  
J. do Ó ◽  
S. Lorca ◽  
J. Sánchez ◽  
P. Ubilla
Keyword(s):  
Elliptic Equation ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Exterior Domains ◽  
Existence And Multiplicity ◽  
Negative Function ◽  
Multiplicity Of Positive Solutions ◽  
Image Position ◽  
Typical Model ◽  
Homogeneous Elliptic Equation

We study the existence and multiplicity of positive solutions of the non-homogeneous elliptic equation where N ≥ 3, the nonlinearity f is superlinear at both zero and infinity, q is a non-trivial, non-negative function, and a and b are non-negative parameters. A typical model is given by f(u) = up, with p ≥ 1.

Three positive solutions for semilinear elliptic problems involving concave and convex nonlinearities

2012 ◽  
Vol 142 (1) ◽  
pp. 115-135 ◽  
Author(s):  
Tsing-San Hsu ◽  
Huei-li Lin
Keyword(s):  
Dirichlet Problem ◽  
Continuous Function ◽  
Positive Solutions ◽  
Smooth Boundary ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic Problems ◽  
Concave And Convex Nonlinearities ◽  
Multiplicity Of Positive Solutions ◽  
Image Position

We study the existence and multiplicity of positive solutions for the Dirichlet problemwhere λ > 0, 1 < q < 2, p = 2* = 2N/(N − 2), 0 ε Ω ⊂ ℝN, N ≥ 3, is a bounded domain with smooth boundary ∂Ω and f is a non-negative continuous function on $\bar{\varOmega}$. Assuming that f satisfies some hypothesis, we prove that the equation admits at least three positive solutions for sufficiently small λ.

scholarly journals MULTIPLE POSITIVE SOLUTIONS OF RESONANT AND NON-RESONANT NON-LOCAL FOURTH-ORDER BOUNDARY VALUE PROBLEMS

2011 ◽  
Vol 54 (1) ◽  
pp. 225-240 ◽  
Author(s):  
J. R. L. WEBB ◽  
M. ZIMA
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Multiple Positive Solutions ◽  
Local Boundary ◽  
Existence And Multiplicity ◽  
Resonant Problem ◽  
Non Local ◽  
Multiplicity Of Positive Solutions ◽  
Image Position

AbstractWe study the existence of positive solutions for equations of the form where 0 < ω < π, subject to various non-local boundary conditions defined in terms of the Riemann–Stieltjes integrals. We prove the existence and multiplicity of positive solutions for these boundary value problems in both resonant and non-resonant cases. We discuss the resonant case by making a shift and considering an equivalent non-resonant problem.

Multiplicity of positive solutions for a class of problems with critical growth in ℝN

2009 ◽  
Vol 52 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Claudianor O. Alves ◽  
Daniel C. de Morais Filho ◽  
Marco A. S. Souto
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Continuous Functions ◽  
Critical Growth ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions ◽  
Image Position

AbstractUsing variational methods, we establish the existence and multiplicity of positive solutions for the following class of problems:where λ,β∈(0,∞), q∈(1,2*−1), 2*=2N/(N−2), N≥3, V,Z:ℝN→ℝ are continuous functions verifying some hypotheses.

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.

Sign in / Sign up

Export Citation Format

Share Document