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Abstract:

We study the existence of large solutions of the semilinear elliptic equation Δu=p(x)f(u) where f is not monotonic. We prove existence, on bounded and unbounded domains, under the assumption that f is Lipschitz continuous, f(0) = 0, f(s) > 0 for s > 0 and there exists a nonnegative, nondecreasing Hölder continuous function g and a constant M such that g(s) ≤ f(s) ≤ Mg(s) for large s. The nonnegative function p is allowed to be zero on much of the domain.

Paper's Title:

The successive approximations method and error estimation in terms of at most the first derivative for delay ordinary differential equations

Author(s):

Alexandru Mihai Bica

Department of Mathematics,
University of Oradea,
Str. Armatei Romane no.5,
410087, Oradea,
Romania
smbica@yahoo.com
abica@uoradea.ro

Abstract:

We present here a numerical method for first order delay ordinary differential equations, which use the Banach's fixed point theorem, the sequence of successive approximations and the trapezoidal quadrature rule. The error estimation of the method uses a recent result of P. Cerone and S.S. Dragomir about the remainder of the trapezoidal quadrature rule for Lipchitzian functions and for functions with continuous first derivative.

Paper's Title:

On Stan Ulam and his Mathematics

Author(s):

Krzysztof Ciesielski and Themistocles M. Rassias

Mathematics Institute, Jagiellonian University,
Łjasiewicza 6, 30-348 Kraków,
Poland
Department of Mathematics. National Technical University of Athens,
Zografou Campus, 15780 Athens,
Greece
Krzysztof.Ciesielski@im.uj.edu.pl
trassias@math.ntua.gr

Abstract:

In this note we give a glimpse of the curriculum vitae of Stan Ulam, his personality and some of the mathematics he was involved in.

Paper's Title:

Ulam Stability of Functional Equations

Author(s):

Stefan Czerwik and Krzysztof Król

Abstract:

In this survey paper we present some of the main results on Ulam-Hyers-Rassias stability for important functional equations.

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