scholarly journals Existence and Multiplicity of Solutions for a Periodic Hill's Equation with Parametric Dependence and Singularities

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Alberto Cabada ◽  
José Ángel Cid
Keyword(s):  
Boundary Value Problem ◽  
Green's Function ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Periodic Boundary Value Problem ◽  
Positive Parameter ◽  
Hill’S Equation ◽  
Parametric Dependence ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

We deal with the existence and multiplicity of solutions for the periodic boundary value problemx″(t)+a(t)x(t)=λg(t)f(x)+c(t), x(0)=x(T), x′(0)=x′(T), whereλis a positive parameter. The functionf:(0,∞)→(0,∞)is allowed to be singular, and the related Green's function is nonnegative and can vanish at some points.

scholarly journals The Existence and Multiplicity of Positive Solutions for Second-Order Periodic Boundary Value Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Feng Wang ◽  
Fang Zhang ◽  
Fuli Wang
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Periodic Boundary Value Problem ◽  
Point Index ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions

The existence and multiplicity of positive solutions are established for second-order periodic boundary value problem. Our results are based on the theory of a fixed point index for A-proper semilinear operators defined on cones due to Cremins. Our approach is different in essence from other papers and the main results of this paper are also new.

scholarly journals Periodic orbits of nonlinear first-order general periodic boundary value problem

Filomat ◽  
2016 ◽  
Vol 30 (13) ◽  
pp. 3427-3434
Author(s):  
Feng Wang ◽  
Fang Zhang ◽  
Hailong Zhu ◽  
Shengjun Li
Keyword(s):  
Boundary Value Problem ◽  
Periodic Orbits ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Degree Theory ◽  
Continuous Functions ◽  
Periodic Boundary Value Problem ◽  
Topological Degree Theory ◽  
First Order ◽  
Existence And Multiplicity

In this paper, the existence and multiplicity of periodic orbits are obtained for first-order general periodic boundary value problem x'(t) + a(t)x(t)=f(t,x), t ? [0,T], x(0)=?x(T), where a : [0,T] ? [0,+?) and f : [0,T]x R+ ? R are continuous functions, ? > 0 and T > 0 with ?e??T,0 a(s)ds=1. The proofs are carried out by the use of topological degree theory. We also prove some nonexistence theorems. Our results extend and improve some recent work in the literature.

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