Existence of solutions for some boundary value problems of fractional \(p\)-Laplacian equation at resonance
type: Item
instance of: scholarly article
title: Existence of solutions for some boundary value problems of fractional \(p\)-Laplacian equation at resonance
zbMATH Open document ID: 1283.34004
author: Jiaying Liu
author: Wenbin Liu
author: Taiyong Chen
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2013-10-21T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bbms/1378314512
reviewed by: Xueyan Liu
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6217256
zbMATH Keywords: fractional differential equation
zbMATH Keywords: \(p\)-Laplacian operator
zbMATH Keywords: Caputo fractional derivative
zbMATH Keywords: boundary value problem
zbMATH Keywords: coincidence degree
zbMATH Keywords: resonance
MaRDI profile type: Publication
review text: The paper is concerned with the existence of solutions of the following two boundary value problems for \(p\)-Laplacian differential equations at resonance: NEWLINE\[NEWLINE D_{0^+}^\beta\phi_p(D_{0^+}^\alpha x(t))=f(t,x(t),D_{0^+}^\alpha x(t)),\quad t\in[0,1], NEWLINE\]NEWLINE NEWLINE\[NEWLINE x(0)=0,\quad D_{0^+}^\alpha x(0)=D_{0^+}^\alpha x(1); NEWLINE\]NEWLINE and NEWLINE\[NEWLINE D_{0^+}^\beta\phi_p(D_{0^+}^\alpha x(t))=f(t,x(t),D_{0^+}^\alpha x(t)),\quad t\in[0,1],NEWLINE\]NEWLINE NEWLINE\[NEWLINE x(1)=0,\quad D_{0^+}^\alpha x(0)=D_{0^+}^\alpha x(1). NEWLINE\]NEWLINE The main tool is the coincidence degree theory. An example is given as an application of their results.
description: scientific article; zbMATH DE number 6217256