Necessary and sufficient conditions for the existence of positive solutions to algebraic Riccati equations with indefinite quadratic term

1992 ◽  
Vol 26 (1) ◽  
pp. 95-110 ◽  
Author(s):  
Shuping Chen
Keyword(s):  
Positive Solutions ◽  
Sufficient Conditions ◽  
Riccati Equations ◽  
Necessary And Sufficient Conditions ◽  
Quadratic Term ◽  
Algebraic Riccati Equations ◽  
Existence Of Positive Solutions ◽  
Indefinite Quadratic ◽  
Necessary And Sufficient

scholarly journals On the existence of positive solutions for periodic parabolic sublinear problems

2003 ◽  
Vol 2003 (17) ◽  
pp. 975-984 ◽  
Author(s):  
T. Godoy ◽  
U. Kaufmann
Keyword(s):  
Bounded Domain ◽  
Positive Solutions ◽  
Wide Class ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Parabolic Problems ◽  
Smooth Bounded Domain ◽  
Carathéodory Functions ◽  
Existence Of Positive Solutions ◽  
Necessary And Sufficient

We give necessary and sufficient conditions for the existence of positive solutions for sublinear Dirichlet periodic parabolic problemsLu=g(x,t,u)inΩ×ℝ(whereΩ⊂ℝNis a smooth bounded domain) for a wide class of Carathéodory functionsg:Ω×ℝ×[0,∞)→ℝsatisfying some integrability and positivity conditions.

scholarly journals The existence of positive solutions for Kirchhoff-type problems via the sub-supersolution method

2018 ◽  
Vol 26 (1) ◽  
pp. 5-41 ◽  
Author(s):  
Baoqiang Yan ◽  
Donal O’Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Positive Solutions ◽  
Bifurcation Theory ◽  
Sufficient Conditions ◽  
Global Bifurcation ◽  
Existence Of A Solution ◽  
Kirchhoff Type ◽  
Existence Of Positive Solutions ◽  
Global Bifurcation Theory ◽  
Necessary And Sufficient ◽  
Kirchhoff Type Problems

Abstract In this paper we discuss the existence of a solution between wellordered subsolution and supersolution of the Kirchhoff equation. Using the sub-supersolution method together with a Rabinowitz-type global bifurcation theory, we establish the existence of positive solutions for Kirchhoff-type problems when the nonlinearity is singular or sign-changing. Moreover, we obtain some necessary and sufficient conditions for the existence of positive solutions for the problem when N = 1.

Extremal Positive Solutions of Semilinear Schrödinger Equations

1983 ◽  
Vol 26 (2) ◽  
pp. 171-178 ◽  
Author(s):  
C. A. Swanson
Keyword(s):  
Differential Equation ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Exterior Domains ◽  
Hölder Continuous ◽  
Semilinear Differential Equation ◽  
Necessary And Sufficient

AbstractNecessary and sufficient conditions are proved for the existence of maximal and minimal positive solutions of the semilinear differential equation Δu = -ƒ(x, u) in exterior domains of Euclidean n-space. The hypotheses are that ƒ(x, u) is nonnegative and Hölder continuous in both variables, and bounded above and below by ugi(| x |, u), i = 1, 2, respectively, where each gi(r, u) is monotone in u for each r > 0.

scholarly journals Asymptotic Behavior of Solutions to Half-Linearq-Difference Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Pavel Řehák
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equation ◽  
Positive Solutions ◽  
Difference Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Special Limit ◽  
Bounded Functions ◽  
Necessary And Sufficient

We derive necessary and sufficient conditions for (some or all) positive solutions of the half-linearq-difference equationDq(Φ(Dqy(t)))+p(t)Φ(y(qt))=0,t∈{qk:k∈N0}withq>1,Φ(u)=|u|α−1sgn⁡uwithα>1, to behave likeq-regularly varying orq-rapidly varying orq-regularly bounded functions (that is, the functionsy, for which a special limit behavior ofy(qt)/y(t)ast→∞is prescribed). A thorough discussion on such an asymptotic behavior of solutions is provided. Related Kneser type criteria are presented.

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