Serdica Mathematical Journal
Volume 23, Number 1, 1997
C O N T E N T S
A B S T R A C T S
OSCILLATION THEOREMS FOR PERTURBED SECOND ORDER
NONLINEAR DIFFERENTIAL EQUATIONS WITH DAMPING
E. M. Elabbasy
1991 Mathematics Subject Classification: 34C10, 34K15.
Key words: oscillatory solutions,
second order differential equations.
Some oscillation criteria for solutions of a
general perturbed second order ordinary differential equation
with damping
(r(t)x¢(t))¢+ h(t)f(x)x¢(t) + y(t,x) = H(t,x(t),x¢(t)) 

with alternating coefficients are given. The results obtained
improve and extend some existing results in the literature.
SOME THEORETICAL RESULTS ON THE PROGENY OF A BISEXUAL
GALTONWATSON BRANCHING PROCESS
M. González, M. Molina
1991 Mathematics Subject Classification: 60J80.
Key words: Bisexual GaltonWatson branching
process, stochastic monotony, total progeny, limit behaviour.
A Superadditive Bisexual GaltonWatson
Branching Process is considered and the total number of mating units,
females and males, until the nth generation, are studied. In particular
some results about the stochastic monotony, probability generating functions
and moments are obtained. Finally, the limit behaviour of those variables
suitably normed is investigated.
MSOLID SUBVARIETIES OF SOME VARIETIES OF COMMUTATIVE
SEMIGROUPS
J. Koppitz
1991 Mathematics Subject Classification: 20M07, 08B15.
Key words: hypersubstitutions, Mhyperidentity,
Msolid subvarieties of semigroups.
The basic concepts are Mhyperidentities, where M is a monoid
of hypersubstitutions. The set of all Msolid varieties of
semigroups forms a complete sublattice of the lattice of all
varieties of semigroups. We fix some specific varieties V of
commutative semigroups and study the set of all Msolid
subvarieties of V, in particular, if V is nilpotent.
ABSTRACT SUBDIFFERENTIAL CALCULUS AND SEMICONVEX FUNCTIONS
Milen Ivanov, Nadia Zlateva
1991 Mathematics Subject Classification:
Primary: 49J52; Secondary 47H04, 47H05.
Key words: nonsmooth calculus, subdifferential, integrability.
We develop an abstract subdifferential calculus for lower semicontinuous
functions and investigate functions similar to convex functions. As
application we give sufficient conditions for the integrability of a
lower semicontinuous function.
ON THE DIFFERENCE OF 4GONAL LINEAR SYSTEMS ON SOME CURVES
Akira Ohbuchi
1991 Mathematics Subject Classification: 14H45, 14H10, 14C20.
Key words: curve theory, algebraic geometry.
Let C=(C,g_{4}^{1}) be a tetragonal curve.
We consider the scrollar invariants
e_{1}, e_{2}, e_{3} of g_{4}^{1}.
We prove that if W_{4}^{1}(C) is a nonsingular
variety, then every g_{4}^{1}Î W_{4}^{1}(C)
has the same scrollar invariants.
EXTREMAL SOLUTIONS FOR A CLASS
OF FUNCTIONAL DIFFERENTIAL EQUATIONS
Rita Ceppitelli, Loris Faina
1991 Mathematics Subject Classification: 34K05, 34A12.
Key words: extremal solutions, hereditary setting,
Carath\'eodory assumptions
We study, in Carathéodory assumptions,
existence, continuation and continuous
dependence of extremal solutions for an abstract and rather general
class of hereditary differential equations. By some examples we prove
that, unlike the nonfunctional case, solved Cauchy problems for
hereditary differential equations may not have local extremal solutions.
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