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

Mathematica Bohemica (2006)

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

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topBereanu, 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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