On Positive Solutions of Nonlinear Third-Order Impulsive Boundary Value Problems on Time Scales

2016 ◽  
Vol 13 (6) ◽  
pp. 4447-4461
Author(s):  
Ilkay Yaslan Karaca ◽  
Fatma Tokmak Fen
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Time Scales ◽  
Boundary Value ◽  
Third Order ◽  
Impulsive Boundary Value Problems

scholarly journals Triple Positive Solutions for Third-Orderm-Point Boundary Value Problems on Time Scales

2009 ◽  
Vol 2009 ◽  
pp. 1-15
Author(s):  
Jian Liu ◽  
Fuyi Xu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Triple Positive Solutions

We study the following third-orderm-point boundary value problems on time scales(φ(uΔ∇))∇+a(t)f(u(t))=0,t∈[0,T]T,u(0)=∑i=1m−2biu(ξi),uΔ(T)=0,φ(uΔ∇(0))=∑i=1m−2ciφ(uΔ∇(ξi)), whereφ:R→Ris an increasing homeomorphism and homomorphism andφ(0)=0,0<ξ1<⋯<ξm−2<ρ(T). We obtain the existence of three positive solutions by using fixed-point theorem in cones. The conclusions in this paper essentially extend and improve the known results.

scholarly journals Multiple positive solutions for nonlinear second-order m-point impulsive boundary value problems on time scales

Filomat ◽  
2015 ◽  
Vol 29 (4) ◽  
pp. 817-827
Author(s):  
Ilkay Karaca ◽  
Fatma Fen
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Time Scales ◽  
Boundary Value ◽  
Index Theory ◽  
Second Order ◽  
Multiple Positive Solutions ◽  
Impulsive Boundary Value Problems ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions

In this paper, by using fixed point index theory, we study the existence of positive solutions for nonlinear second-order m-point impulsive boundary value problems on time scales. As an application, we give an example to demonstrate our results.

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