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Existence of solutions of integral equations with asymptotic conditions [PDF]

Nonlinear Analysis: Real World Applications, 2018
In this work we will consider integral equations defined on the whole real line and look for solutions which satisfy some certain kind of asymptotic behavior. To do that, we will define a suitable Banach space which, to the best of our knowledge, has never been used before.
Lucía López-Somoza, Alberto Cabada, F. Adrián F. Tojo   +2 more
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Asymptotic Solutions of Linear Volterra Integral Equations With Singular Kernels [PDF]

Transactions of the American Mathematical Society, 1974
Volterra integral equations of the form u ′ ( t ) = − ∫ 0 t a ( t − τ ) u ( τ ) d τ , u ( 0 ) = 1 u’(t) = - \smallint _0^ta(
J. S. W. Wong, Roderick Wong
  +5 more sources

Asymptotic Solutions of Integral Equations with Convolution Kernels [PDF]

Proceedings of the Edinburgh Mathematical Society, 1964
SummaryThe equations considered are Fredholm integral equations of the second kind with regular kernels, whose argument depends only on the difference of the variables. Approximate solutions are sought for a given finite range of the eigenvalues, and for large values of the range of integration.
V. Hutson
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Linear integral equations with asymptotically almost periodic solutions

Journal of Mathematical Analysis and Applications, 1975
AbstractConditions are given that ensure that bounded solutions of ∫−ξξ x(t − ξ)dA(ξ) = ƒ(t) are asymptotically almost periodic. The result strengthens and extends a recent theorem of Levin and Shea. Generalizations to systems of integral equations as well as to integrodifferential systems are included.
G. S. Jordan, Robert L. Wheeler
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Asymptotics of the Solutions to Singularly Perturbed Integral Equations

Journal of Mathematical Analysis and Applications, 1993
The authors study the asymptotics of \(h_ \varepsilon\) as \(\varepsilon \to 0\), where \(h_ \varepsilon\) is a solution of the integral equation \((*)\) \(\varepsilon h_ \varepsilon+Rh_ \varepsilon=f\), \(\varepsilon>0\), \(Rh_ \varepsilon(x)=\int^ \beta_ \alpha R(x-y)h_ \varepsilon(y)dy\) with \(R(x)=P(D)G(x)\), \(P(D)=\sum^ p_{j=0}a_ jD^ j\), \(D=d ...
Alexander G. Ramm, E.I. Shifrin
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Asymptotic behavior of unbounded solutions of linear Volterra integral equations

Journal of Mathematical Analysis and Applications, 1976
AbstractThe asymptotic behavior as t → ∞ of solutions of ∝0tu(t − s) dA(s) = f(t) is studied when f(t) satisfies a “o” estimate as t ” ∞, and A belongs to a weighted space and its Laplace-Stieltjes transform has finitely many zeros in its closed half-plane of convergence.
Robert L Wheeler, Robert L Wheeler, G. S. Jordan   +2 more
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Linear Convolution Integral Equations with Asymptotically Almost Periodic Solutions [PDF]

Proceedings of the American Mathematical Society, 1980
Let μ \mu be a bounded Borel measure and f be asymptotically almost periodic. Conditions are found which ensure that certain bounded solutions of the linear convolution integral equation g ∗ μ = f g \ast \mu = f are asymptotically almost periodic.
R. L. Wheeler, G. S. Jordan, W. R. Madych   +2 more
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Asymptotically exponential solutions in nonlinear integral and differential equations

Journal of Differential Equations, 2010
AbstractIn this paper we investigate the growth/decay rate of solutions of an abstract integral equation which frequently arises in quasilinear differential equations applying a variation-of-constants formula. These results are applicable to some abstract equations which appear in the theory of age-dependent population models and also to some ...
Ferenc Hartung, István Győri
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EXISTENCE AND ASYMPTOTIC STABILITY OF SOLUTIONS TO A FUNCTIONAL-INTEGRAL EQUATION [PDF]

Taiwanese Journal of Mathematics, 2007
Using the Darbo’s fixed-point theorem associated with the measure of noncompactness due to Bana´s, we establish the existence and asymptotic stability of solutions for a functional-integral equation. An example which shows the importance of our result is also included.
Liu, Zeqing, Kang, Shin Min
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Asymptotic Behavior of Solutions to a Vector Integral Equation with Deviating Arguments [PDF]

Abstract and Applied Analysis, 2013
In this paper, we propose the study of an integral equation, with deviating arguments, of the typey(t)=ω(t)-∫0∞‍f(t,s,y(γ1(s)),…,y(γN(s)))ds,t≥0,in the context of Banach spaces, with the intention of giving sufficient conditions that ensure the existence of solutions with the same asymptotic behavior at∞asω(t).
Cristóbal González, Antonio Jiménez-Melado   +1 more
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