scholarly journals Existence of Positive Solutions for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

2021 ◽  
Vol 12 (04) ◽  
pp. 311-321
Author(s):  
Alhussein Mohamed
Keyword(s):  
Green’S Function ◽  
Positive Solutions ◽  
Green's Function ◽  
Fourth Order ◽  
Existence Of Positive Solutions

scholarly journals Positive Solutions for a Fractional Boundary Value Problem with a Perturbation Term

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
Yumei Zou
Keyword(s):  
Boundary Value Problem ◽  
Green’S Function ◽  
Positive Solutions ◽  
Green's Function ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Perturbation Term ◽  
Existence Of Positive Solutions

We obtain some new upper and lower estimates for the Green’s function associated with a fractional boundary value problem with a perturbation term. Criteria for the existence of positive solutions of the problem are then obtained based on it.

scholarly journals Existence of Positive Solutions for Nonlinear Third-Order Boundary Value Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Tiaoxia Dun ◽  
Pengyu Chen
Keyword(s):  
Boundary Value Problem ◽  
Green’S Function ◽  
Positive Solutions ◽  
Green's Function ◽  
Boundary Value ◽  
Index Theorem ◽  
Third Order ◽  
Existence Of Positive Solutions ◽  
Fixed Point Index Theorem ◽  
Linear Boundary Value Problem

We are concerned with the existence of positive solutions for the nonlinear third-order three-point boundary value problemu′′′(t)+λg(t)f(u(t))=0,0<t<1,u(0)=αu(η),u′(0)=u′′(1)=0, where0<η<1,0<α<1,λis a positive parameter,g:(0,1)→[0,∞),  and  f:[0,∞)→[0,∞)is continuous. We construct Green’s function for the associated linear boundary value problem and obtain some useful properties of Green’s function. Finally, by using fixed-point index theorem in cones, we establish the existence results of positive solutions for the boundary value problem an example illustrates the application of the results obtained.

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