01341nas a2200133   4500008004100000245011300041210006900154260003400223520083400257100002301091700002301114700001901137856005101156       2018                        en  d00aPositive solutions for super-sublinear indefinite problems: high multiplicity results via coincidence degree0 aPositive solutions for supersublinear indefinite problems high m  bAmerican Mathematical Society3 a<p>We study the periodic boundary value problem associated with the second order nonlinear equation u''+(λa+(t)−μa−(t))g(u)=0, where g(u) has superlinear growth at zero and sublinear growth at infinity. For λ,μ positive and large, we prove the existence of 3^m−1 positive T-periodic solutions when the weight function a(t) has m positive humps separated by m negative ones (in a T-periodicity interval). As a byproduct of our approach we also provide abundance of positive subharmonic solutions and symbolic dynamics. The proof is based on coincidence degree theory for locally compact operators on open unbounded sets and also applies to Neumann and Dirichlet boundary conditions. Finally, we deal with radially symmetric positive solutions for the Neumann and the Dirichlet problems associated with elliptic PDEs.</p>1 aBoscaggin, Alberto1 aFeltrin, Guglielmo1 aZanolin, Fabio  uhttp://urania.sissa.it/xmlui/handle/1963/35264