Geodesic
Existence and multiplicity results for nonlinear second order difference equations with Dirichlet boundary conditions
Mathematica Bohemica, Tome 131 (2006) no. 2, pp. 145-160.

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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.
DOI : 10.21136/MB.2006.134087
Classification : 39A11, 47H11, 47N20
Keywords: nonlinear difference equations; Ambrosetti-Prodi problem; Brouwer degree 
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Bereanu, Cristian; Mawhin, Jean. Existence and multiplicity results for nonlinear second order difference equations with Dirichlet boundary conditions. Mathematica Bohemica, Tome 131 (2006) no. 2, pp. 145-160. doi : 10.21136/MB.2006.134087. http://geodesic.mathdoc.fr/articles/10.21136/MB.2006.134087/

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