Positive Solutions to Nonlinear Higher-Order Nonlocal Boundary Value Problems for Fractional Differential Equations
We study existence of positive solutions to nonlinear higher-order nonlocal boundary value problems corresponding to fractional differential equation of the type 𝑐𝒟𝛿0+𝑢(𝑡)+𝑓(𝑡,𝑢(𝑡))=0, 𝑡∈(0,1), 0<𝑡<1. 𝑢(1)=𝛽𝑢(𝜂)+𝜆2, 𝑢(0)=𝛼𝑢(𝜂)−𝜆1, 𝑢(0)=0, 𝑢(0)=0⋯𝑢(𝑛−1)(0)=0, where, 𝑛−1<𝛿<𝑛, 𝑛(≥3)∈ℕ,...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/501230 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We study existence of positive solutions to nonlinear higher-order nonlocal
boundary value problems corresponding to fractional differential equation of the type 𝑐𝒟𝛿0+𝑢(𝑡)+𝑓(𝑡,𝑢(𝑡))=0, 𝑡∈(0,1), 0<𝑡<1. 𝑢(1)=𝛽𝑢(𝜂)+𝜆2, 𝑢(0)=𝛼𝑢(𝜂)−𝜆1, 𝑢(0)=0, 𝑢(0)=0⋯𝑢(𝑛−1)(0)=0, where, 𝑛−1<𝛿<𝑛, 𝑛(≥3)∈ℕ, 0<𝜂,𝛼,𝛽<1, the boundary parameters 𝜆1,𝜆2∈ℝ+ and 𝑐𝐷𝛿0+ is the Caputo fractional derivative. We use the classical tools from functional analysis to obtain
sufficient conditions for the existence and uniqueness of positive solutions to the boundary value
problems. We also obtain conditions for the nonexistence of positive solutions to the problem. We
include examples to show the applicability of our results. |
|---|---|
| ISSN: | 1085-3375 1687-0409 |