Positive solutions for nonlocal differential equations with concave and convex coefficients

IF 0.8 3区数学 Q2 MATHEMATICS

Positivity Pub Date : 2024-09-16 DOI:10.1007/s11117-024-01086-9

Qingcong Song, Xinan Hao

引用次数: 0

Abstract

In this paper, we study the positive solutions for nonlocal differential equations with concave and convex coefficients:

$$\begin{aligned} -A\left( \int ^1_0 (u^p(s)+u^q(s))ds\right) u''(t)=f(t,u(t)),\quad t\in (0,1), \end{aligned}$$

where $0<p<1\le q.$ Using the fixed point index theory and fixed point theorems on cones, existence and multiplicity results are obtained, when the nonlinear term f(t, x) is continuous, has a singularity at $x=0$, changes sign, respectively.

查看原文本刊更多论文

具有凹凸系数的非局部微分方程的正解

本文研究了具有凹凸系数的非局部微分方程的正解：$$\begin{aligned} -A\left( \int ^1_0 (u^p(s)+u^q(s))ds\right) u''(t)=f(t,u(t)),\quad t\in (0,1), \end{aligned}$$ 其中 $0<p<1\le q.$ 当非线性项f(t, x)是连续的、在$x=0$处有奇点、符号改变时，利用锥体上的定点索引理论和定点定理，分别得到了存在性和多重性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Positivity 数学-数学

CiteScore

1.80

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： The purpose of Positivity is to provide an outlet for high quality original research in all areas of analysis and its applications to other disciplines having a clear and substantive link to the general theme of positivity. Specifically, articles that illustrate applications of positivity to other disciplines - including but not limited to - economics, engineering, life sciences, physics and statistical decision theory are welcome. The scope of Positivity is to publish original papers in all areas of mathematics and its applications that are influenced by positivity concepts.