Measures of noncompactness, darbo maps and differential equations in abstract spaces
Copyright policy )Measures of noncompactness, darbo maps and differential equations in abstract spaces
Let \(B\) be a real Banach space. The existence theory for the initial value problem \(y'(t)= q(t) f(t, y(t))\), \(t\in (0, T]\), \(y(0)= a\in B\), \(q\in C (0, T]\), \(q>0\) and \(\int^T_0 q(s) ds0\) and \(\int^1_0 q(s)ds< \infty\) is considered in the case when \(f\) has a splitting of the form \(f= g+h\) with \(g\), \(h\) continuous and \(g\) satisfying some compactness condition. The existence theory is based on a Leray-Schauder type nonlinear alternative [see \textit{J. Dugundji} and \textit{A. Granas}, Fixed point theory. Warszawa (1982; Zbl 0483.47038)] and on the Kuratowski measure of noncompactness.
- University of Galway Ireland
Dirichlet boundary value problem, Banach space, Nonlinear boundary value problems for ordinary differential equations, Kuratowski measure of noncompactness, Leray-Schauder type nonlinear alternative, Nonlinear differential equations in abstract spaces, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, initial value problem
Dirichlet boundary value problem, Banach space, Nonlinear boundary value problems for ordinary differential equations, Kuratowski measure of noncompactness, Leray-Schauder type nonlinear alternative, Nonlinear differential equations in abstract spaces, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, initial value problem
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).5 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.Average
Citations provided by BIP!Popularity provided by BIP!