Weak and strong topologies and integral equations in Banach spaces

We give sufficient conditions for the existence of at least one integrable solution of equation $x (t) = f (t) + \int_{0}^{t} K (t, s) g (s, x (s)) d s$ . Our assumptions and proofs are expressed in terms of measures of noncompactness.

Qualitative properties of nonlinear Volterra integral equations.

Islam, M., Neugebauer, J.T. (2008)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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Unbounded solutions of a boundary value problem for abstract $n$ th-order differential equations on an infinite interval.

Liu, Zhenbin, Liu, Lishan, Wu, Yonghong, Zhao, Jing (2008)

Journal of Applied Mathematics and Stochastic Analysis

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Integral equations with contrasting kernels.

Burton, T.A. (2008)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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On positive solutions of a class of second order nonlinear differential equations on the halfline

Svatoslav Staněk (1995)

Annales Polonici Mathematici

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The differential equation of the form ${(q (t) k (u) {(u^{'})}^{a})}^{'} = f (t) h (u) u^{'}$ , a ∈ (0,∞), is considered and solutions u with u(0) = 0 and (u(t))² + (u’(t))² > 0 on (0,∞) are studied. Theorems about existence, uniqueness, boundedness and dependence of solutions on a parameter are given.