Results 11 to 20 of about 585 (118)
On a nonlinear Volterra integral equation
Journal of Differential Equations, 1973 Also note the comments. made on (1.1) in [2]. More recently Eq. (1.1) has been analyzed in [I and 31 under hypotheses related to those of Theorem I. Comparing the present result with the results of [3] we observe the following. In addition to the full hypothesis of Theorem 1 above, certain smoothness conditions were imposed on a(t) and f(i) in [3 ...
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Qualitative properties of nonlinear Volterra integral equations
Electronic Journal of Qualitative Theory of Differential Equations, 2008 Summary: The contraction mapping principle and Lyapunov's method are used to study qualitative properties of nonlinear Volterra equations of the form \[ x(t) = a(t) -\int^{t}_{0}C(t,s)g(s,x(s))\;ds,\quad t\geq0. \] In particular, the existence of bounded solutions and solutions with various \(L^p\) properties are studied under suitable conditions on ...
Islam, Muhammad, Neugebauer, J.
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Oscillation Theorems of Nonlinear Volterra-Stieltjes Integral Equations
Journal of Mathematical Analysis and Applications, 1995 The oscillatory behavior of solutions to the nonlinear Volterra-Stieltjes integral equation \[ p(t) \psi (y) y'_+ (t)= c+ \int^t_0 f(y (s)) d\sigma (s) \] is considered. \(y'_+ (t)\) denotes the right derivative of \(y(t)\), \(p(t)> 0\) and \(\sigma (t)\) are right-continuous and of locally bounded variation on \([0, \infty)\), \(\psi: (- \infty ...
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A Note on Volterra Integral Equations with Power Nonlinearity
Journal of Integral Equations and Applications, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Niedziela, M., Okrasiński, W.
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A Starting Method for Solving Nonlinear Volterra Integral Equations [PDF]
Mathematics of Computation, 1967 In this paper a fifth order starting method is given for Volterra equations of the form y ( t ) = f ( t ) + ∫ x 0 t k ( t
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On some Nonlinear Integral Inequalities for Volterra Integral Equations
Annals of the Alexandru Ioan Cuza University - Mathematics, 2014 Abstract In this paper, we have stated and proved some results on nonlinear integral inequalities and its applications which provide an explicit bound on unknown function and can be used as a tool in the study of certain nonlinear retarded Volterra integral equations.
S.D. Kendre, S.G. Latpate
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Solving volterra integral equation via nonlinear programming
International Journal of Applied Mathematical Research, 2016 In this paper we propose an approach to find approximate solution to the nonlinear Volterra integral equation of the second type through a nonlinear programming technique by firstly converting the integral equation into a least square cost function as an objective function for an unconstrained nonlinear programming problem which solved by a nonlinear ...
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Solutions for certain nonlinear Volterra integral equations
Journal of Mathematical Analysis and Applications, 1979 where t belongs to a half open (possibly unbounded) interval I = (0, c), and u, + and f have values in R*, the m-dimensional Euclidean space with the norm I x I = 1 x1 / + ... + I xm I when x = (xl,..., x”). We shall give three main local existence theorems, Theorem 2.1-2.3, under very general assumptions on f.
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Collocation Method for Nonlinear Volterra-Fredholm Integral Equations
Open Journal of Applied Sciences, 2012 A fully discrete version of a piecewise polynomial collocation method based on new collocation points, is constructed to solve nonlinear Volterra-Fredholm integral equations. In this paper, we obtain existence and uniqueness results and analyze the convergence properties of the collocation method when used to approximate smooth solutions of Volterra ...
Jafar Ahmadi Shali +2 more
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Volterra Runge- Kutta Methods for Solving Nonlinear Volterra Integral Equations
Baghdad Science Journal, 2010 In this paper Volterra Runge-Kutta methods which include: method of order two and four will be applied to general nonlinear Volterra integral equations of the second kind. Moreover we study the convergent of the algorithms of Volterra Runge-Kutta methods.
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