Abstract
We arranged the problem μ″ + f(u)=g(x) where f is a real C2 smooth function with n simple zeroes z1,…,zn and g is a C2 smooth function wnich maps [0,π] in R and satisfies a certain smaiiness condition relative to f We show that if n is even problem (∗) has at least n−1 solutions; if n is odd, problem (∗) has at least n solutions if f′(z1) 0. We also obtain estimates of the range of these solutions and calculate the stable ones (stable as stationary solutions of an associated diffusion problem) with a simple numerical method
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