Existence and multiplicity results for nonlinear second order difference equations with Dirichlet boundary conditions

Cristian Bereanu; Jean Mawhin

Mathematica Bohemica (2006)

  • Volume: 131, Issue: 2, page 145-160
  • ISSN: 0862-7959

Abstract

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We use Brouwer degree to prove existence and multiplicity results for the solutions of some nonlinear second order difference equations with Dirichlet boundary conditions. We obtain in particular upper and lower solutions theorems, Ambrosetti-Prodi type results, and sharp existence conditions for nonlinearities which are bounded from below or from above.

How to cite

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Bereanu, Cristian, and Mawhin, Jean. "Existence and multiplicity results for nonlinear second order difference equations with Dirichlet boundary conditions." Mathematica Bohemica 131.2 (2006): 145-160. <http://eudml.org/doc/249917>.

@article{Bereanu2006,
abstract = {We use Brouwer degree to prove existence and multiplicity results for the solutions of some nonlinear second order difference equations with Dirichlet boundary conditions. We obtain in particular upper and lower solutions theorems, Ambrosetti-Prodi type results, and sharp existence conditions for nonlinearities which are bounded from below or from above.},
author = {Bereanu, Cristian, Mawhin, Jean},
journal = {Mathematica Bohemica},
keywords = {nonlinear difference equations; Ambrosetti-Prodi problem; Brouwer degree; Ambrosetti-Prodi problem; Brouwer degree; nonlinear second order difference equations; upper and lower solutions theorems},
language = {eng},
number = {2},
pages = {145-160},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence and multiplicity results for nonlinear second order difference equations with Dirichlet boundary conditions},
url = {http://eudml.org/doc/249917},
volume = {131},
year = {2006},
}

TY - JOUR
AU - Bereanu, Cristian
AU - Mawhin, Jean
TI - Existence and multiplicity results for nonlinear second order difference equations with Dirichlet boundary conditions
JO - Mathematica Bohemica
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 131
IS - 2
SP - 145
EP - 160
AB - We use Brouwer degree to prove existence and multiplicity results for the solutions of some nonlinear second order difference equations with Dirichlet boundary conditions. We obtain in particular upper and lower solutions theorems, Ambrosetti-Prodi type results, and sharp existence conditions for nonlinearities which are bounded from below or from above.
LA - eng
KW - nonlinear difference equations; Ambrosetti-Prodi problem; Brouwer degree; Ambrosetti-Prodi problem; Brouwer degree; nonlinear second order difference equations; upper and lower solutions theorems
UR - http://eudml.org/doc/249917
ER -

References

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  13. Ambrosetti-Prodi type results in nonlinear boundary value problems, Differential equations and mathematical physics. Lect. Notes in Math. 1285, Springer, Berlin, 1987, pp. 290–313. (1987) Zbl0651.34014MR0921281
  14. A simple approach to Brouwer degree based on differential forms, Advanced Nonlinear Studies 4 (2004), 535–548. (2004) Zbl1082.47052MR2100911
  15. Uniqueness for boundary value problems for second order finite difference equations, J. Differ. Equations Appl. 10 (2004), 749–757. (2004) MR2069640
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  17. The nonexistence of spurious solutions to discrete, two-point boundary value problems, Appl. Math. Lett. 16 (2003), 79–84. (2003) MR1938194

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