MULTIPLE POSITIVE SOLUTIONS FOR A p-LAPLACIAN DIRICHLET PROBLEM WITH SUPERDIFFUSIVE REACTION

作者：Aizicovici Sergiu^*; Papageorgiou Nikolaos S; Staicu Vasile

来源：Houston Journal of Mathematics, 2010, 36(1): 313-333.

• p-Laplacian
• superdiffusive reaction
• positive solutions
• multiple solutions
• strong comparison principle
• nonlinear maximum principle
• nonlinear regularity

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.

• 出版日期2010