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

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