Positive solutions for nonlocal differential equations with concave and convex coefficients
type: Item
instance of: scholarly article
title: Positive solutions for nonlocal differential equations with concave and convex coefficients
author: Qingcong Song
author: Xinan Hao
published in: Positivity
publication date: 2024-10-28T00:00:00Z
review text: In this paper the authors study the positive solutions for nonlocal differential equations with concave and convex coefficients \N\[\N-A\left(\int_0^1(u^p(s)+u^q(s))\mathrm{d}s\right)u''(t)=f(t,u(t)),\quad t\in(0,1), \N\]\Nwhere the function \(A:\mathbb{R}\to\mathbb{R}\) is continuous, \(0<p<1\leq q\), the nonlinear term \(f(t,x)\) is continuous, has a singularity at \(x=0\) and changes sign. The authors obtained the existence and multiplicity results of above problem by using the fixed point index theory and fixed point theorems on cones.
reviewed by: Minghe Pei
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 47H11
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 7932489
zbMATH Keywords: nonlocal differential equation
zbMATH Keywords: nonlocal boundary condition
zbMATH Keywords: concave and convex coefficients
zbMATH Keywords: positive solution
zbMATH Keywords: fixed point
MaRDI profile type: Publication
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DOI: 10.1007/S11117-024-01086-9
description: scientific article; zbMATH DE number 7932489