01084nas a2200121   4500008004100000245013700041210006900178260002300247520059900270100002300869700001900892856005100911       2015                        en  d00aExistence of positive solutions in the superlinear case via coincidence degree: the Neumann and the periodic boundary value problems0 aExistence of positive solutions in the superlinear case via coin  bKhayyam Publishing3 a<p>We prove the existence of positive periodic solutions for the second order nonlinear equation u'' + a(x) g(u) = 0, where g(u) has superlinear growth at zero and at infinity. The weight function a(x) is allowed to change its sign. Necessary and sufficient conditions for the existence of nontrivial solutions are obtained. The proof is based on Mawhin's coincidence degree and applies also to Neumann boundary conditions. Applications are given to the search of positive solutions for a nonlinear PDE in annular domains and for a periodic problem associated to a non-Hamiltonian equation.</p>1 aFeltrin, Guglielmo1 aZanolin, Fabio  uhttp://projecteuclid.org/euclid.ade/1435064518