scholarly journals Existence and Nonexistence of Positive Solutions for High-Order Fractional Differential Equation Boundary Value Problems at Resonance

2020 ◽  
Vol 2020 ◽  
pp. 1-10 ◽  
Author(s):  
Yongqing Wang ◽  
Huiqing Wang
Keyword(s):  
Boundary Value Problems ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
High Order ◽  
At Resonance ◽  
Nonexistence And Existence ◽  
Equation Boundary ◽  
Fixed Point Index Theory ◽  
Fractional Differential

We investigate positive solution for high-order fractional differential equations with resonant boundary value conditions. By using the spectral theory and the fixed point index theory, both the nonexistence and existence results of the resonant boundary value problems are given.

scholarly journals Existence, Nonexistence and Multiplicity of Positive Solutions for Singular Boundary Value Problems Involving φ-Laplacian

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 953 ◽  
Author(s):  
Chan-Gyun Kim
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Interesting Point ◽  
Fixed Point Index Theory ◽  
Multiplicity Of Positive Solutions

In this paper, we establish the results on the existence, nonexistence and multiplicity of positive solutions to singular boundary value problems involving φ -Laplacian. Our approach is based on the fixed point index theory. The interesting point is that a result for the existence of three positive solutions is given.

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 Multiple Solutions for Boundary Value Problems of th-Order Nonlinear Integrodifferential Equations in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yanlai Chen
Keyword(s):  
Boundary Value Problems ◽  
Multiple Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Integrodifferential Equations ◽  
Point Index ◽  
Three Solutions ◽  
Equations Of Mixed Type ◽  
Fixed Point Index Theory

The boundary value problems of a class of th-order nonlinear integrodifferential equations of mixed type in Banach space are considered, and the existence of three solutions is obtained by using the fixed-point index theory.

scholarly journals Multiple Solutions for a Class of Nonlinear Fourth-Order Boundary Value Problems

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1989
Author(s):  
Longfei Lin ◽  
Yansheng Liu ◽  
Daliang Zhao
Keyword(s):  
Boundary Value Problems ◽  
Fourth Order ◽  
Multiple Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
The Other ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Special Cone

This paper is concerned with multiple solutions for a class of nonlinear fourth-order boundary value problems with parameters. By constructing a special cone and applying fixed point index theory, the multiple solutions for the considered systems are obtained under some suitable assumptions. The main feature of obtained solutions (u(t),v(t)) is that the solution u(t) is positive, and the other solution v(t) may change sign. Finally, two examples with continuous function f1 being positive and f2 being semipositone are worked out to illustrate the main results.

scholarly journals Positive solutions of a discrete second-order boundary value problems with fully nonlinear term

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Liyun Jin ◽  
Hua Luo
Keyword(s):  
Positive Solutions ◽  
Fixed Point Index ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Index Theory ◽  
Second Order ◽  
Fully Nonlinear ◽  
Fixed Point Index Theory ◽  
Weaker Conditions ◽  
Lower Limits

Abstract In this paper, we mainly consider a kind of discrete second-order boundary value problem with fully nonlinear term. By using the fixed-point index theory, we obtain some existence results of positive solutions of this kind of problems. Instead of the upper and lower limits condition on f, we may only impose some weaker conditions on f.

scholarly journals On a singular Riemann–Liouville fractional boundary value problem with parameters

2021 ◽  
Vol 26 (1) ◽  
pp. 151-168
Author(s):  
Alexandru Tudorache ◽  
Rodica Luca
Keyword(s):  
Fixed Point ◽  
Fixed Point Index ◽  
Nonlocal Boundary ◽  
Index Theory ◽  
Nonlocal Boundary Conditions ◽  
Principal Characteristic ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions ◽  
Semipositone Problem ◽  
Fractional Differential

We investigate the existence of positive solutions for a nonlinear Riemann–Liouville fractional differential equation with a positive parameter subject to nonlocal boundary conditions, which contain fractional derivatives and Riemann–Stieltjes integrals. The nonlinearity of the equation is nonnegative, and it may have singularities at its variables. In the proof of the main results, we use the fixed point index theory and the principal characteristic value of an associated linear operator. A related semipositone problem is also studied by using the Guo–Krasnosel’skii fixed point theorem.

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