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 Positive solutions of three-point boundary value problems for higher-orderp-Laplacian with infinitely many singularities

2006 ◽  
Vol 2006 ◽  
pp. 1-12 ◽  
Author(s):  
Fuyi Xu ◽  
Yonghong Wu ◽  
Lishan Liu ◽  
Yunming Zhou
Keyword(s):  
Fixed Point ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Index Theorem ◽  
Point Boundary ◽  
Point Index ◽  
Fixed Point Index Theorem ◽  
Infinitely Many Singularities

We study a three-point nonlinear boundary value problem with higher-orderp-Laplacian. We show that there exist countable many positive solutions by using the fixed point index theorem for operators in a cone.

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.

scholarly journals A Generalization of Mahadevan's Version of the Krein-Rutman Theorem and Applications top-Laplacian Boundary Value Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yujun Cui ◽  
Jingxian Sun
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Boundary Value Problems ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Point Index ◽  
Homogeneous Operator ◽  
Existence Of Positive Solutions ◽  
Positive Eigenfunction ◽  
Homogeneous Operators

We will present a generalization of Mahadevan’s version of the Krein-Rutman theorem for a compact, positively 1-homogeneous operator on a Banach space having the properties of being increasing with respect to a conePand such that there is a nonzerou∈P∖{θ}−Pfor whichMTpu≥ufor some positive constantMand some positive integerp. Moreover, we give some new results on the uniqueness of positive eigenvalue with positive eigenfunction and computation of the fixed point index. As applications, the existence of positive solutions forp-Laplacian boundary-value problems is considered under some conditions concerning the positive eigenvalues corresponding to the relevant positively 1-homogeneous operators.

EXISTENCE OF MULTIPLE POSITIVE SOLUTIONS FOR p-LAPLACIAN PROBLEMS WITH A GENERAL INDEFINITE WEIGHT

2008 ◽  
Vol 10 (03) ◽  
pp. 337-362 ◽  
Author(s):  
CHAN-GYUN KIM ◽  
YONG-HOON LEE
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Singular Boundary ◽  
Multiple Positive Solutions ◽  
Singular Boundary Value Problems ◽  
Indefinite Weight ◽  
Point Index ◽  
Existence Of Positive Solutions

This paper studies the existence of positive solutions for a class of singular boundary value problems of p-Laplacian. By using Global Continuation Theorem and the fixed point index technique, criteria of the existence, multiplicity and nonexistence of positive solutions are established.

Existence, multiplicity and non-existence of positive solutions for two-point boundary-value problems with strong singularity

2010 ◽  
Vol 140 (6) ◽  
pp. 1187-1196
Author(s):  
Chan-Gyun Kim
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Point Boundary ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions ◽  
Image Position

We study the existence, multiplicity and non-existence of positive solutions for the singular two-point boundary-value problemswhere $\varphi_{p}(s)=|s|^{p-2}s$, $p>1$, λ is a non-negative real parameter and f ∈ C((0, 1) × [0,∞), (0,∞)). Here, f(t, u) may be singular at t = 0 and/or 1. To obtain the main results we use the global continuation theorem and fixed-point index theory.

scholarly journals Positive Solutions for a System of Nonlinear Semipositone Boundary Value Problems with Riemann-Liouville Fractional Derivatives

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaowei Qiu ◽  
Jiafa Xu ◽  
Donal O’Regan ◽  
Yujun Cui
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fractional Derivatives ◽  
Fixed Point Index ◽  
Existence Theorems ◽  
Boundary Value ◽  
Point Index ◽  
Coupling Behavior ◽  
Existence Of Positive Solutions ◽  
Liouville Fractional Derivative

We study the existence of positive solutions for the system of nonlinear semipositone boundary value problems with Riemann-Liouville fractional derivatives D0+αD0+αu=f1t,u,u′,v,v′,  0<t<1, D0+αD0+αv=f2(t,u,u′,v,v′),  0<t<1, u0=u′0=u′(1)=D0+αu(0)=D0+α+1u(0)=D0+α+1u(1)=0, and v(0)=v′(0)=v′(1)=D0+αv(0)=D0+α+1v(0)=D0+α+1v(1)=0, where α∈(2,3] is a real number and D0+α is the standard Riemann-Liouville fractional derivative of order α. Under some appropriate conditions for semipositone nonlinearities, we use the fixed point index to establish two existence theorems. Moreover, nonnegative concave and convex functions are used to depict the coupling behavior of our nonlinearities.

Existence of positive solutions to multi-point third order problems with sign changing nonlinearities

2020 ◽  
Vol 24 (1) ◽  
pp. 109-129
Author(s):  
Abdulkadir Dogan ◽  
John R. Graef
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Point Index ◽  
Third Order ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions

In this paper, the authors examine the existence of positive solutions to a third-order boundary value problem having a sign changing nonlinearity. The proof makes use of fixed point index theory. An example is included to illustrate the applicability of the results.

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