We prove that appropriate combinations of superlinearity and sublinearity of f(u) with respect to Φ at zero and infinity guarantee the existence, multiplicity, and nonexistence of positive solutions to boundary value problems for the n-dimensional system (Φ(u′) ′ + λh(t)f(u) = 0, 0 < t < 1. The vector-valued function Φ is defined by Φ(u′) = ( (u1′ ,..., (un′)), where u = (u1,...,un and covers the two important cases (u′) = u′ and (u′) = u′ p-2u′, p > 1. Our methods employ fixed point theorems in a cone.
ASJC Scopus subject areas
- Applied Mathematics