Generalized boundary value problems with linear growth

Valter Šeda

Mathematica Bohemica (1998)

  • Volume: 123, Issue: 4, page 385-404
  • ISSN: 0862-7959

Abstract

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It is shown that for a given system of linearly independent linear continuous functionals l i C n - 1 → ℝ , i = 1 , ⋯ , 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.

How to cite

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Šeda, Valter. "Generalized boundary value problems with linear growth." Mathematica Bohemica 123.4 (1998): 385-404. <http://eudml.org/doc/248296>.

@article{Šeda1998,
abstract = {It is shown that for a given system of linearly independent linear continuous functionals $l_i C^\{n-1\} \rightarrow \mathbb \{R\}$, $i=1,\dots ,n$, 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.},
author = {Šeda, Valter},
journal = {Mathematica Bohemica},
keywords = {generic properties; periodic boundary value problem; generic properties; periodic boundary value problem},
language = {eng},
number = {4},
pages = {385-404},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generalized boundary value problems with linear growth},
url = {http://eudml.org/doc/248296},
volume = {123},
year = {1998},
}

TY - JOUR
AU - Šeda, Valter
TI - Generalized boundary value problems with linear growth
JO - Mathematica Bohemica
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 123
IS - 4
SP - 385
EP - 404
AB - It is shown that for a given system of linearly independent linear continuous functionals $l_i C^{n-1} \rightarrow \mathbb {R}$, $i=1,\dots ,n$, 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.
LA - eng
KW - generic properties; periodic boundary value problem; generic properties; periodic boundary value problem
UR - http://eudml.org/doc/248296
ER -

References

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