Nonlinear integral equations singular in the dependent variable
Copyright policy )Nonlinear integral equations singular in the dependent variable
This paper concerns the existence of nonnegative solutions to the singular integral equation \(y(t)=\int^1_0 k(t,s)[G(s,y(s))+F(s,y(s))]ds\) \((t\in [0,1])\), where \(G\in C([0,1]\times (0,\infty),[0,\infty))\), \(F\in C([0,1]\times [0,\infty),[0,\infty))\) so \(G\) may be singular at \(y=0\). By using a well-known existence principle based on the Leray-Schauder alternative, the authors present a general existence result, which improves essentially the result of \textit{R. P. Agarwal} and \textit{D. O'Regan} [ZAMM, Z. Angew. Math. Mech. 81, No. 7, 499--504 (2001; Zbl 0988.45005)].
- Florida Institute of Technology United States
- National University of Ireland Ireland
- University of Galway Ireland
Second order boundary value problems, nonlinear singular integral equation, Applied Mathematics, Positive solutions of integral equations, Singular nonlinear integral equations, Singular integral equations, Leray-Schauder alternative, Nonnegative solutions, Leray–Schauder alternative, nonnegative solutions, second order boundary value problems
Second order boundary value problems, nonlinear singular integral equation, Applied Mathematics, Positive solutions of integral equations, Singular nonlinear integral equations, Singular integral equations, Leray-Schauder alternative, Nonnegative solutions, Leray–Schauder alternative, nonnegative solutions, second order boundary value problems
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).13 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!