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2 edition of Existence and uniqueness theorems for a nonlinear integral equation. found in the catalog.

Existence and uniqueness theorems for a nonlinear integral equation.

Roberto Ramalho

Existence and uniqueness theorems for a nonlinear integral equation.

by Roberto Ramalho

  • 258 Want to read
  • 15 Currently reading

Published by Universidade Federal de Pernambuco, Instituto de Matemática in Recife [Brazil] .
Written in English

    Subjects:
  • Integral equations.

  • Edition Notes

    Bibliography: leaf 42.

    SeriesNotas e comunicações de matemática,, no. 40
    Classifications
    LC ClassificationsQA1 .N863 no. 40, QA431 .N863 no. 40
    The Physical Object
    Pagination42 l.
    Number of Pages42
    ID Numbers
    Open LibraryOL5454538M
    LC Control Number73156728

      Existence and uniqueness of fixed points of a mapping defined on partially ordered G-metric spaces is discussed. The mapping satisfies contractive conditions based on certain classes of functions. The results are applied to the problems involving contractive conditions of integral type and to a particular type of initial value problems for the nonhomogeneous heat equation in one by: 1.   Uniqueness of solutions to an Abel type nonlinear integral equation on the half line Measures of noncompactness in the study of solutions of nonlinear differential and integral equations A generalization of Krasnosel’skii fixed point theorem for sums of Cited by: 3.

      In recent years, the existence and uniqueness theorems of solutions for boundary value problems of nonlinear fractional differential equations have been studied extensively in the literature, mainly by using the fixed point theorem of the mixed-monotone operator (see, for instance, [7, 18, 33, 34] and their references), a priori estimate method Cited by:   As an application, the received results are used to summarize the existence and uniqueness of the solution for nonlinear Fredholm integral equations. The purpose of this work is to establish new fixed point theorems for generalized contraction mappings with respect to w-distances in complete metric spaceAuthor: Teerawat Wongyat, Wutiphol Sintunavarat.

    The space of nonempty compact sets of is well-known to be a nonlinear space. This fact essentially complicates the research of set-valued differential and integral equations. In this article we consider set-valued Volterra integral equations and prove the existence and uniqueness theorem. X. Yu, Liouville type theorems for integral equations and integral systems,, \emph{Calculus of Variations and Partial Differential Equations}, 46 (), doi: /sz. Cited by: 5.


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Existence and uniqueness theorems for a nonlinear integral equation by Roberto Ramalho Download PDF EPUB FB2

Existence and Uniqueness Theorems for a Class of Non-Linear Singular Integral Equations with Application to a Hydroelastic Problem RONALD FINNILA & JAMES M. SLOSS Communicated by J. Keller Introduction. In this paper we shall be concerned with showing the existence and uniqueness of a solution, in the class of complex-valued Holder continuous.

Integral Equation Uniqueness Theorem Nonlinear Integral Equation These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm by: 6. Theorems of Existence and Uniqueness for Nonlinear Fredholm and Volterra Integral Equations for Functions with Values in L-spaces Vira Babenko Abstract.

Existence and uniqueness theorems for a nonlinear integral equation. book We consider nonlinear integral equations of Fredholm and Volterra type with respect to functions having values in L-spaces.

Such class of equations includes set-valued integral equations, fuzzy. THEOREMS OF EXISTENCE AND UNIQUENESS FOR NONLINEAR FREDHOLM AND VOLTERRA INTEGRAL EQUATIONS FOR FUNCTIONS WITH VALUES IN L. THEOREMS OF EXISTENCE AND UNIQUENESS FOR NONLINEAR FREDHOLM AND VOLTERRA INTEGRAL EQUATIONS FOR FUNCTIONS WITH VALUES IN L-SPACES.

VIRA BABENKO ABSTRACT. We consider nonlinear integral equations of Fredholm. Existence and uniqueness theorems for a certain class of non-linear singular integral equations. Complex Variables and Elliptic Equations: Vol. 51, No. 2, pp. Cited by: 2. INTRODUCTION It was shown by Bauer [l] that the Perron definition of the integral [7] is a generalization of the Lebesgue integral.

In this paper the Perron integral is used to establish an existence and uniqueness theorem for the differential equation Du (z) = f [z, u (ss)] a.e. (almost everywhere) onJ (1) with boundary conditions u (x, 0) == a (x), u (0,y)=b (y), and a (0) == & (0) (2) where I = {z = (x, y) \ 0 Cited by: 1.

In this paper, we intend to prove the existence and uniqueness of the solutions of the following nonhomogeneous nonlinear Volterra integral equation: where, is a mapping, and is a continuous function on the domain.

The solutions of integral equations have a major role in the fields of science and engineering [ by: 6. and because f (x, y) = x 2 cos x + y / x is not continuous on an interval containing x = 0, the Existence and Uniqueness theorem does not guarantee the existence or uniqueness of a solution.

In fact, using DSolve we see that a general solution of the equation is y = x sin x + C x. In this work, we establish new fixed point theorems for w-generalized weak contraction mappings with respect to w-distances in complete metric spaces by using the concept of an altering distance function.

As an application, we use the obtained results to aggregate the existence and uniqueness of the solution for nonlinear Fredholm integral equations and Volterra integral equations Cited by: 4.

equivalen t set integral equations. However, integral equations are encoun tered in various. fields of science and in numerous applications, including elasticity, plasticity, heat and.

mass. Chapter 4 Existence and uniqueness of solutions for nonlinear ODEs In this chapter we consider the existence and uniqueness of solutions for the initial value problem for general nonlinear ODEs.

Recall that it is this property that underlies the existence of a ow. We only consider the problem for autonomous ODEs, but note that through ( File Size: KB.

conditions for existence and uniqueness of solutions and diffeomorphism of a nonlinear vector function is reported. Thus there is a need to work on specific vector functional form of the non-linear equation for the study of existence, uniqueness and C' − diffeomorphic solution of the problems.

Existence and Uniqueness Theorems for Nth Order Linear and Nonlinear Integral Equations Showing of 46 pages in this thesis. PDF Version Also Available for Download. Description. The purpose of this paper is to study nth order integral equations.

The integrals Author: Gayle Jene Shultz Hurlbert. and [5], and in some detail for the nonlinear case by Erdelyi [6].

Theorem in this thesis is a result for nonlinear Volterra integral equations similar to Erdelyi's result in [6], but differing enough to warrant a separate proof. Theorem is used to get our main integral equation result Theorem THE EXISTENCE AND UNIQUENESS OF THE SOLUTION FOR NONLINEAR FREDHOLM AND VOLTERRA INTEGRAL EQUATIONS VIA ADAPTING-CEILING DISTANCES TEERAWAT WONGYAT, WUTIPHOL SINTUNAVARAT Abstract.

The purpose of this work is to introduce the new contractive con-dition which involves mw-distances in metric spaces. The xed point theorems. In this work, we performed an study about the domain of existence and uniqueness for an efficient fifth order iterative method for solving nonlinear problems treated in their infinite dimensional form.

The hypotheses for the operator and starting guess are weaker than in the previous studies. We assume omega continuity condition on second order Fréchet : Sukhjit Singh, Eulalia Martínez, Abhimanyu Kumar, D.

Gupta. Lieb, Existence and uniqueness of the minimizing solution of Choquard's nonlinear equation, Studies in Appl.

Math., 57 (/77), doi: /sapm Google ScholarCited by: 4. Fixed point theory is one of the most efficient tools in nonlinear functional analysis to solve the nonlinear differential and integral equations.

The existence/uniqueness of a solution of differential/integral equations turns into the existence/uniqueness of a (common) fixed point of the operators which are obtained after suitable Cited by: 6.

Since, therefore is a contraction. Hence, by Banach contraction principle, has a unique fixed point in such that, which is a solution of the coupled integral equations () and ().This completes the proof.

The following Corollary ensures the uniqueness of the solutions of ().Cited by: The existence and uniqueness of solutions for nonlinear ordinary differential equation with noninstantaneous impulses is obtained by using perturbation technique, monotone iterative method and a new estimation technique of the measure of noncompactness under the situation that the corresponding noninstantaneous impulsive functions g i are Author: Xuping Zhang.

In the present study, the nonlocal and integral boundary value problems for the system of nonlinear fractional differential equations involving the Caputo fractional derivative are investigated.

Theorems on existence and uniqueness of a solution are established under some sufficient conditions on nonlinear terms. A simple example of application of the main result of this paper is by: engineering 1, 2. A physical event can be modeled by the differential equation, an integral equation, an integrodifferential equation, or a system of these 3, 4.

Investigation on ex-istence theorems for diverse nonlinear functional-integral equations has been presented in other references such as 5–Comment: The existence and uniqueness theorem are also valid for certain system of rst order equations. These theorems are also applicable to a certain higher order ODE since a higher order ODE can be reduced to a system of rst order ODE.

Example 1. Consider the ODE y0= xy siny; y(0) = 2: Here fand @[email protected] continuous in a closed rectangle about xFile Size: 78KB.