The aim of the present paper is to give existence results for some multi-point value problems with nonlinear boundary conditions (BVP for short) regarding second order ordinary differential equations. In particular the author by using the Nonlinear Alternative of the well-known Topological Transversality and a variation of the well-known Leray-Schauder Alternative in a different way without using the a-priori bounds on all relevant solutions of the related one parameter family of problems produces a {|it ``forbidden value''} of the norm of solutions, that is, a value which the norm never takes on. (The original result is given in theorem 3.1). Moreover many examples may be derived from the general form of the existence results based on specific BVP problems.

Στοιχεία Άρθρου

Περιοδικό	Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
Αρ. Τεύχους	Τεύχος 43
Περίοδος	2000
Συγγραφέας	P. Ch. Tsamatos
Αρ. Αρθρου	4
Σελίδες	71-79
Γλώσσα	-
Λέξεις Κλειδιά	multi-point value problems, nonlinear alternative

Multi-Point Boundary Value Problems with Nonlinear Boundary Conditions