Multiple positive solutions for a p-Laplacian Dirichlet problem with superdiffusive reaction
Sergiu Aizicovici, Nikolaos S. Papageorgiou, Vasile Staicu · 2010
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 lambda* > 0, such that for every parameter lambda >= lambda*, the problem has a strictly positive smooth solution. Subsequently, by strengthening the conditions on the Caratheodory nonlinearity f(z ,x) (see (P-lambda) below), it is shown that for all lambda >= lambda* the problem has two positive solutions.