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a.e in ft a.e. in ft2 Ai(fta Ai(m,ft associated to principal Assume f given blow-up alternative Blow-up solutions Campinas Caratheodory function concave convergence convex Corollary 1.9 defined Dirichlet boundary condition equation 1.1 exist a constant f satisfies Filidor following result given by 1.3 Global solutions Hq(Q infix integrating J.M. Martinez Jensen's inequality Jn Jn Jn Jn3 Jn3 Jose Plinio Juliana Cervelati Lemma Lr(ft M.L. Schuverdt Marcelo F Mari Sano Marko Martinez and M.L. maximal interval 0,Tmax maximal positive solution maximal solution Metric Spaces Minimal Nodal Solutions Multiplying 1.1 nondecreasing nonempty open set nonincreasing nonnegative function nonnegative solution Números de Fibonacci principal eigenfunction associated principal eigenvalue problem 1.1 proposition 2.1 Quasilinear Remark Rojas-Medar Sandra Augusta Santos satisfies the equation sense of 1.8 Sobolev solution for uo solution of 1.1 subsolution supersolution of 1.1 t>o Jn Theorem 1.4 Tmax un(t uo satisfies 1.7 valid Young's inequalities