The positive solutions of boundary value problems for a class of one-dimensional image-Laplacians Original Research Article

This paper is concerned with the exact number of positive solutions for boundary value problems (|u′|p−2u′)′+λf(u)=0(|u′|p−2u′)′+λf(u)=0 and u(−1)=u(1)=0u(−1)=u(1)=0, where p>1p>1 and λ>0λ>0 is a positive parameter. We consider the case in which the nonlinearity ff changes sign from positive to negative on (0,∞)(0,∞). For example, f(u)=uα−uβf(u)=uα−uβ where β>α>−∞β>α>−∞.