122164103
A comparison theorem for difference inequalities
In the study of growth and decay properties of nonlinear evolution equations (in particular hyperbolic and parabolic partial differential equations) as t → ∞, the following difference inequality (which is satisfied by an energy expression) arises: 
 
$$(*)\mathop {\sup }\limits_{t \leq s \leq t + 1} u{(s)^{1 + \alpha }} \leq c{(1 + t)^r}(u(t) - u(t + 1)) + g(t)$$ 
 
(*) 
 
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122832071
THERE IS AN ELEMENTARY PROOF OF PEANO'S EXISTENCE THEOREM.
Abstract : An elementary, constructive proof of Peano's existence theorem is given. The maximal solution is constructed as a limit of a decreasing sequence of approximate solutions. (Author)
120951143
Verallgemeinerte Laplace-Operatoren und Potentiale
122666640
Remarks on a paper by F. Browder about contraction
THROUGHOUT this note, X denotes a complete metric space with distance function d, and T is a map from X into itself. Powers of T are defined by Tax = x and T”+ lx = T(T”x), n 2 0. Occasionally, we use the notation xk = Tkx, in particular x0 = x, x1 = TX, for the sake of brevity. The set {x, TX, T'x, . . . , T”x,. . .} is called an orbit (starting at x) and denoted by O(x). The set 0(x, y) is the union of the two orbits starting at x and y, 0(x, y) = {xk, yk: k 3 O}. The diameter diam A of a nonempty subset A of X is the supremum of the numbers d(x, y), where x and y vary in A. The letter 4 denotes a contractive gauge function, i.e. a continuous, increasing function from R,, the non-negative reals, into R, which satisfies 4(s) 0.
119881926
Fehlerabschätzungen und Eindeutigkeitssätze für gewöhnliche und partielle Differentialgleichungen
123298075
Eindeutigkeitssätze für gewöhnliche, parabolische und hyperbolische Differentialgleichungen
1300115
Flexible precision control and dynamic data structures for programming mathematical and numerical algorithms