Existence of Positive Solutions for Nonlinear Third-Order m-Point Impulsive Boundary-Value Problems on Time Scales

2016 ◽  
Vol 68 (3) ◽  
pp. 458-474
Author(s):  
I. Y. Karaca ◽  
F. T. Fen
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Time Scales ◽  
Boundary Value ◽  
Third Order ◽  
Impulsive Boundary Value Problems ◽  
Existence Of Positive Solutions

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.

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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