**
MATHEMATICA BOHEMICA, Vol. 131, No. 2, pp. 145-160 (2006)
**

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

Dirichlet boundary conditions

##
Cristian Bereanu, Jean Mawhin

* Cristian Bereanu*, * Jean Mawhin*, Departement de Mathematique, Universite Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium, e-mail: ` mawhin@ math.ucl.ac.be`

**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.

**Keywords:** nonlinear difference equations, Ambrosetti-Prodi problem, Brouwer degree

**Classification (MSC2000):** 39A11, 47H11

**Full text of the article:**

[Previous Article] [Next Article] [Contents of this Number] [Journals Homepage]

*
© 2006–2010
FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition
*