Multiple solutions for a class of fractional boundary value problems
type: Item
instance of: scholarly article
title: Multiple solutions for a class of fractional boundary value problems
zbMATH Open document ID: 1253.34009
DOI: 10.1155/2012/468980
author: Ge Bin
published in: Abstract and Applied Analysis
publication date: 2012-12-18T00:00:00Z
review text: Summary: We study the multiplicity of solutions for the following fractional boundary value problem: \((d/dt)((1/2)_0D^{-\beta}_t(u'(t)) + (1/2)_0D^{-\beta}_T(u'(t))) + \lambda \nabla F(t, u(t)) = 0\), a.e. \(t \in [0, T], u(0) = u(T) = 0\) where \(_0D^{-\beta}_t\) and \(_0D^{-\beta}_T\) are the left and right Riemann-Liouville fractional integrals of order \(0 \leq \beta < 1\), respectively, \(\lambda > 0\) is a real number, \(F : [0, T] \times \mathbb R^N \rightarrow \mathbb R\) is a given function, and \(\nabla F(t, x)\) is the gradient of \(F\) at \(x\). The approach used in this paper is the variational method. More precisely, the Weierstrass theorem and mountain pass theorem are used to prove the existence of at least two nontrivial solutions.
Mathematics Subject Classification ID: 34A08
zbMATH DE Number: 6116406
zbMATH Keywords: fractional boundary value problem
zbMATH Keywords: variational method
zbMATH Keywords: Weierstrass theorem
MaRDI profile type: Publication
Wikidata QID: Q58695246
full work available at URL: https://doi.org/10.1155/2012/468980
OpenAlex ID: W2139379703
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description: scientific article; zbMATH DE number 6116406