scholarly journals Existence of Positive Solutions to Singular φ-Laplacian Nonlocal Boundary Value Problems when φ is a Sup-multiplicative-like Function

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 420 ◽  
Author(s):  
Jeongmi Jeong ◽  
Chan-Gyun Kim
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Index Theorem ◽  
Multiple Positive Solutions ◽  
Nonlocal Boundary Value Problems ◽  
Existence Of Positive Solutions ◽  
Fixed Point Index Theorem

In this paper, using a fixed point index theorem on a cone, we present some existence results for one or multiple positive solutions to φ -Laplacian nonlocal boundary value problems when φ is a sup-multiplicative-like function and the nonlinearity may not satisfy the L 1 -Carath e ´ odory condition.

Positive Solutions for Nonlinear Lidstone Boundary Value Problems

2013 ◽  
Vol 313-314 ◽  
pp. 1201-1204 ◽  
Author(s):  
Lei Wang ◽  
Li Li
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Existence Result ◽  
Boundary Value ◽  
Index Theorem ◽  
Point Index ◽  
Existence Of Positive Solutions ◽  
Fixed Point Index Theorem

In this paper, we consider the existence of positive solutions for nonlinear Lidstone boundary value problems. An new existence result is obtained by applying the fixed point index theorem.

scholarly journals Multiple Positive Solutions of a Singular Semipositone Integral Boundary Value Problem for Fractionalq-Derivatives Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Yulin Zhao ◽  
Guobing Ye ◽  
Haibo Chen
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Index Theorem ◽  
Multiple Positive Solutions ◽  
Integral Boundary ◽  
Integral Boundary Value Problem ◽  
Fixed Point Index Theorem

By using the fixed point index theorem, this paper investigates a class of singular semipositone integral boundary value problem for fractionalq-derivatives equations and obtains sufficient conditions for the existence of at least two and at least three positive solutions. Further, an example is given to illustrate the applications of our main results.

scholarly journals Positive solutions of some nonlocal boundary value problems

2003 ◽  
Vol 2003 (18) ◽  
pp. 1047-1060 ◽  
Author(s):  
Gennaro Infante ◽  
J. R. L. Webb
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Point Boundary ◽  
General Behaviour ◽  
Nonlocal Boundary Value Problems ◽  
Existence Of Positive Solutions

We establish the existence of positive solutions of somem-point boundary value problems under weaker assumptions than previously employed. In particular, we do not require all the parameters occurring in the boundary conditions to be positive. Our results allow more general behaviour for the nonlinear term than being either sub- or superlinear.

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.

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.

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