Multiple positive solutions for a p-Laplacian Dirichlet problem with superdiffusive reaction

• Autores: Sergiu Aizicovici, Nikolaos S. Papageorgiou, Vasile Staicu
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 36, Nº 1, 2010, págs. 313-333
• Idioma: inglés
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• Resumen

  • A parametric Dirichlet elliptic problem, driven by the p-Laplacian, and with a superdiffusive reaction is studied. First, it is shown that there exists a ?* > 0, such that for every parameter ? ??*, the problem has a strictly positive smooth solution. Subsequently, by strengthening the conditions on the Caratheodory nonlinearity f(z,x) that appears in the equation under consideration, it is shown that for all ? > ?* the problem has two positive solutions.