Nonlocal systems of BVPs with asymptotically superlinear boundary conditions

Christopher S. Goodrich

Commentationes Mathematicae Universitatis Carolinae (2012)

  • Volume: 53, Issue: 1, page 79-97
  • ISSN: 0010-2628

Abstract

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In this paper we consider a coupled system of second-order boundary value problems with nonlocal, nonlinear boundary conditions, and we examine conditions under which such problems will have at least one positive solution. By imposing only an asymptotic growth condition on the nonlinear boundary functions, we are able to achieve generalizations over existing works and, in particular, we allow for the nonlocal terms to be able to be realized as Lebesgue-Stieltjes integrals possessing signed Borel measures. We conclude with a numerical example to illustrate the use of one of our two main results.

How to cite

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Goodrich, Christopher S.. "Nonlocal systems of BVPs with asymptotically superlinear boundary conditions." Commentationes Mathematicae Universitatis Carolinae 53.1 (2012): 79-97. <http://eudml.org/doc/246207>.

@article{Goodrich2012,
abstract = {In this paper we consider a coupled system of second-order boundary value problems with nonlocal, nonlinear boundary conditions, and we examine conditions under which such problems will have at least one positive solution. By imposing only an asymptotic growth condition on the nonlinear boundary functions, we are able to achieve generalizations over existing works and, in particular, we allow for the nonlocal terms to be able to be realized as Lebesgue-Stieltjes integrals possessing signed Borel measures. We conclude with a numerical example to illustrate the use of one of our two main results.},
author = {Goodrich, Christopher S.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {coupled system of second-order boundary value problems; nonlocal boundary condition; nonlinear boundary condition; superlinear growth; positive solution; coupled system; nonlocal boundary condition; nonlinear boundary condition; superlinear growth; positive solution},
language = {eng},
number = {1},
pages = {79-97},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Nonlocal systems of BVPs with asymptotically superlinear boundary conditions},
url = {http://eudml.org/doc/246207},
volume = {53},
year = {2012},
}

TY - JOUR
AU - Goodrich, Christopher S.
TI - Nonlocal systems of BVPs with asymptotically superlinear boundary conditions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 1
SP - 79
EP - 97
AB - In this paper we consider a coupled system of second-order boundary value problems with nonlocal, nonlinear boundary conditions, and we examine conditions under which such problems will have at least one positive solution. By imposing only an asymptotic growth condition on the nonlinear boundary functions, we are able to achieve generalizations over existing works and, in particular, we allow for the nonlocal terms to be able to be realized as Lebesgue-Stieltjes integrals possessing signed Borel measures. We conclude with a numerical example to illustrate the use of one of our two main results.
LA - eng
KW - coupled system of second-order boundary value problems; nonlocal boundary condition; nonlinear boundary condition; superlinear growth; positive solution; coupled system; nonlocal boundary condition; nonlinear boundary condition; superlinear growth; positive solution
UR - http://eudml.org/doc/246207
ER -

References

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