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Now showing items 41-50 of 65

#### Remarks on Nonlinear Contraction and Comparison Principle in Abstract Cones

(University of Texas at Arlington, 1975-06)

The contraction mapping principle and the Schauder principle can both be viewed as a comparison of maps. For the former one has a condition of the type [see pdf for notation] and for the latter one has a condition of the ...

#### On a Measure of Nonconvexity and Applications

(University of Texas at Arlington, 1975-06)

The measure of noncompactness which was introduced by Kuratowski [8] (in 1930) has now become an important tool in nonlinear analysis (although its value in that regard was not appreciated until much later). Following ...

#### On Massera Type Converse Theorem in Terms of Two Different Measures (0)

(University of Texas at Arlington, 1975)

The importance of uniform asymptotic stability in studying the stability properties of perturbed motions needs no emphasis. The converse theorem of Massera which results from uniform asymptotic stability has been widely ...

#### On the Redundancy of Monotony Assumption

(University of Texas at Arlington, 1974-07)

It is well known that all the results in integral inequalities of Bellman-Gronwall-Reid type demand an assumption of monotony on the functions involved. Since the corresponding theory of differential inequalities does not ...

#### Method of Quasi-Upper and Lower Solutions in Abstract Cones

(University of Texas at Arlington, 1981-05)

Let E be a real Banach space with ||•|| and let E* denote the dual of E. Let K C E be a cone, that is, a closed convex subset such
that ^K C K for every ^ ≥ 0 and K ^ {-K} = {O}, By means of K a partial order ≤ is defined ...

#### Sobolev Type Differential Equations

(University of Texas at Arlington, 1977-06)

An imbedding method for solving linear Fredholm integral equations was introduced by Sobolev [3] which involves the solution of the following differential equation with initial value for the resolvent kernel [see pdf for ...

#### Existence MD Estimates for Solutions of Nonlinear Equations Near a Branch Point

(University of Texas at Arlington, 1973-12)

Consider the equation (1.1) [see pdf for notation]
on a Hilbert space H. Here n is a scalar and [see pdf for notation] is a linear Fredholm operator. That is:
(a) L is closed; (b) The domain, D(L) is dense in H;
(c) The ...

#### On the Existence of Solutions of Differential Equations of Retarded Type in a Banach Space

(University of Texas at Arlington, 1975-06)

The existence and uniqueness of solutions of differential equations of retarded type in a Banach space are considered under a monotonicity type condition. The tools that are available for the study of equations without ...

#### A Technic in Perturbation Theory

(University of Texas at Arlington, 1974-07)

A study of the effect of perturbations of differential equations depends on the method employed and on the nature of perturbations. One of the most used technics is that of Lyapunov method and the other is the nonlinear ...

#### Systems by the Method of Quasisolutions

(University of Texas at Arlington, 1981-01)

Recently [10] the method of lower and upper solutions has been
extended to systems of reaction diffusion equations which has
become very useful in dealing with applications. This extension
depends crucially on a ...