MATHEMATICA BOHEMICA, Vol. 123, No. 4, pp. 385-404 (1998)

Generalized boundary value problems
with linear growth

Valter Seda

Valter Seda, Department of Mathematical Analysis, Comenius University, Mlynska dolina, 842 15 Bratislava, Slovakia, e-mail:

Abstract: It is shown that for a given system of linearly independent linear continuous functionals $l_i C^{n-1} \to\bb R$, $i=1,\dots,n$, the set of all $n$-th order linear differential equations such that the Green function for the corresponding generalized boundary value problem (BVP for short) exists is open and dense in the space of all $n$-th order linear differential equations. Then the generic properties of the set of all solutions to nonlinear BVP-s are investigated in the case when the nonlinearity in the differential equation has a linear majorant. A periodic BVP is also studied.

Keywords: generic properties, periodic boundary value problem

Classification (MSC2000): 34B15

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