scholarly journals POSITIVE SOLUTIONS OF P-LAPLACIAN M-POINT BOUNDARY VALUE PROBLEMS ON TIME SCALES

2008 ◽  
Vol 12 (1) ◽  
pp. 105-127 ◽  
Author(s):  
Hong-Rui Sun ◽  
Wan-Tong Li
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Time Scales ◽  
Boundary Value ◽  
Point Boundary

scholarly journals Successive Iteration and Positive Solutions for Nonlinearm-Point Boundary Value Problems on Time Scales

2009 ◽  
Vol 2009 ◽  
pp. 1-13
Author(s):  
Yanbin Sang
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Time Scales ◽  
Boundary Value ◽  
Point Boundary ◽  
Iterative Schemes ◽  
Monotone Iterative ◽  
Successive Iteration ◽  
Existence Of Positive Solutions ◽  
Cone Expansion And Compression

We study the existence of positive solutions for a class ofm-point boundary value problems on time scales. Our approach is based on the monotone iterative technique and the cone expansion and compression fixed point theorem of norm type. Without the assumption of the existence of lower and upper solutions, we do not only obtain the existence of positive solutions of the problem, but also establish the iterative schemes for approximating the solutions.

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.

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