8.—On Second-order Differential Inequalities

1974 ◽  
Vol 72 (2) ◽  
pp. 109-127 ◽  
Author(s):  
F. V. Atkinson
Keyword(s):  
Differential Equations ◽  
Positive Solutions ◽  
Second Order ◽  
Differential Inequalities ◽  
Existence Of Positive Solutions ◽  
Image Position

SynopsisThis paper is devoted to a study of differential equations and inequalities of the formandThe results are mainly concerned with the existence of positive solutions, their uniqueness in the case of (*), and bounds for these solutions.

T-periodic solutions for some second order differential equations with singularities

1992 ◽  
Vol 120 (3-4) ◽  
pp. 231-243 ◽  
Author(s):  
Manuel del Pino ◽  
Raúl Manásevich ◽  
Alberto Montero
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Positive Solutions ◽  
Resonance Condition ◽  
Second Order ◽  
Fredholm Alternative ◽  
Positive Slope ◽  
Second Order Differential Equations ◽  
Image Position

SynopsisWe study the existence of T-periodic positive solutions of the equationwhere f(t, .) has a singularity of repulsive type near the origin. Under the assumption that f(t, x) lies between two lines of positive slope for large and positive x, we find a non-resonance condition which predicts the existence of one T-periodic solution.Our main result gives a Fredholm alternative-like result for the existence of T-periodic positive solutions for

scholarly journals Positive Solutions of Nonresonant Singular Boundary Value Problem of Second Order Differential Equations

2001 ◽  
Vol 162 ◽  
pp. 127-148 ◽  
Author(s):  
Zhongli Wei ◽  
Changci Pang
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Second Order Differential Equations ◽  
Existence Of Positive Solutions ◽  
Necessary And Sufficient

This paper investigates the existence of positive solutions of nonresonant singular boundary value problem of second order differential equations. A necessary and sufficient condition for the existence of C[0, 1] positive solutions as well as C1[0, 1] positive solutions is given by means of the method of lower and upper solutions with the fixed point theorems.

scholarly journals Oscillation theorems for semilinear hyperbolic and ultrahyperbolic operators

1978 ◽  
Vol 18 (1) ◽  
pp. 55-64 ◽  
Author(s):  
Mamoru Narita
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Differential Inequalities ◽  
Hyperbolic Operator ◽  
Oscillation Property ◽  
All Solutions ◽  
Existence Of Positive Solutions ◽  
Image Position ◽  
Oscillation Theorems

The oscillation property of the semilinear hyperbolic or ultra-hyperbolic operator L defined byis studied. Sufficient conditions are provided for all solutions of uL[u] ≤ 0 satisfying certain boundary conditions to be oscillatory. The basis of our results is the non-existence of positive solutions of the associated differential inequalities.

scholarly journals APPLICATIONS OF VARIATIONAL METHODS TO BOUNDARY-VALUE PROBLEM FOR IMPULSIVE DIFFERENTIAL EQUATIONS

2008 ◽  
Vol 51 (2) ◽  
pp. 509-527 ◽  
Author(s):  
Yu Tian ◽  
Weigao Ge
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Variational Methods ◽  
Positive Solutions ◽  
Boundary Value ◽  
Impulsive Differential Equations ◽  
Impulsive Effects ◽  
Differential Inequalities ◽  
Existence Of Positive Solutions ◽  
Sturm Liouville

AbstractIn this paper, we investigate the existence of positive solutions to a second-order Sturm–Liouville boundary-value problem with impulsive effects. The ideas involve differential inequalities and variational methods.

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