scholarly journals Positive solutions for singular nonlocal boundary value problems involving integral conditions with derivative dependence

2015 ◽  
Vol 23 (2) ◽  
pp. 279-304 ◽  
Author(s):  
Baoqiang Yan ◽  
Donal O’Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fixed Point Theory ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Point Theory ◽  
Multiple Positive Solutions ◽  
Integral Conditions ◽  
Nonlocal Boundary Value Problems

Abstract In this paper using a fixed point theory on a cone we present some new results on the existence of multiple positive solutions for singular nonlocal boundary value problems involving integral conditions with derivative dependence.

scholarly journals The existence of multiple positive solutions of p-Laplacian boundary value problems

2007 ◽  
Vol 57 (3) ◽  
Author(s):  
Yuji Liu
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Sufficient Conditions ◽  
Multiple Positive Solutions ◽  
Nonlocal Boundary Value Problems

AbstractIn this paper, we establish sufficient conditions to guarantee the existence of at least three or 2n − 1 positive solutions of nonlocal boundary value problems consisting of the second-order differential equation with p-Laplacian (1) $$[\phi _p (x'(t))]' + f(t,x(t)) = 0, t \in (0,1),$$ and one of following boundary conditions (2) $$x(0) = \int\limits_0^1 {x(s) dh(s),} \phi _p (x'(1)) = \int\limits_0^1 {\phi _p (x'(s)) dg(s)} ,$$ and (3) $$\phi _p (x'(0)) = \int\limits_0^1 {\phi _p (x'(s)) dh(s),} x(1) = \int\limits_0^1 {x(s) dg(s)} .$$ Examples are presented to illustrate the main results.

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