Some necessary and sufficient conditions for existence of positive solutions for third order singular super-linear multi-point boundary value problems

2014 ◽  
Vol 46 (1-2) ◽  
pp. 407-422
Author(s):  
Zhongli Wei
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Point Boundary ◽  
Third Order ◽  
Existence Of Positive Solutions ◽  
Necessary And Sufficient

scholarly journals Positive solutions of fourth-order superlinear singular boundary value problems

2002 ◽  
Vol 66 (1) ◽  
pp. 95-104 ◽  
Author(s):  
Guoliang Shi ◽  
Shaozhu Chen
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fourth Order ◽  
Closed Interval ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Singular Boundary ◽  
Point Boundary ◽  
Singular Boundary Value Problems ◽  
Necessary And Sufficient

This paper investigates fourth-order superlinear singular two-point boundary value problems and obtains necessary and sufficient conditions for existence of C2 or C3 positive solutions on the closed interval.

scholarly journals Positive Solutions of Two-Point Boundary Value Problems for Monge-Ampère Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Baoqiang Yan ◽  
Meng Zhang
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Existence Of Positive Solutions ◽  
Necessary And Sufficient ◽  
Monge Ampere

This paper considers the following boundary value problem:((-u'(t))n)'=ntn-1f(u(t)),  0<t<1,  u'(0)=0,  u(1)=0, wheren>1is odd. We establish the method of lower and upper solutions for some boundary value problems which generalizes the above equations and using this method we present a necessary and sufficient condition for the existence of positive solutions to the above boundary value problem and some sufficient conditions for the existence of positive solutions.

scholarly journals Positive Solutions for Third-Order Nonlinearp-Laplacianm-Point Boundary Value Problems on Time Scales

2008 ◽  
Vol 2008 ◽  
pp. 1-16 ◽  
Author(s):  
Fuyi Xu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Time Scales ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Point Boundary ◽  
Third Order ◽  
Existence Of Positive Solutions

We study the following third-orderp-Laplacianm-point boundary value problems on time scales:(ϕp(uΔ∇))∇+a(t)f(t,u(t))=0,t∈[0,T]T,βu(0)−γuΔ(0)=0,u(T)=∑i=1m−2aiu(ξi),ϕp(uΔ∇(0))=∑i=1m−2biϕp(uΔ∇(ξi)), whereϕp(s)isp-Laplacian operator, that is,ϕp(s)=|s|p−2s,p>1,  ϕp−1=ϕq,1/p+1/q=1,  0<ξ1<⋯<ξm−2<ρ(T). We obtain the existence of positive solutions by using fixed-point theorem in cones. The conclusions in this paper essentially extend and improve the known results.

scholarly journals Existence of positive solutions for nonlinear third-order m-point boundary value problems on time scales

Filomat ◽  
2014 ◽  
Vol 28 (5) ◽  
pp. 925-935
Author(s):  
Ilkay Karacaa ◽  
Fatma Tokmaka
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Time Scales ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Growth Conditions ◽  
Point Boundary ◽  
Double Positive ◽  
Third Order ◽  
Existence Of Positive Solutions

In this paper, we investigate the existence of double positive solutions for nonlinear third-order m-point boundary value problems with p-Laplacian on time scales. By using double fixed point theorem, we establish results on the existence of two positive solutions with suitable growth conditions imposed on the nonlinear term. As an application, we give an example to demonstrate our main result.

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