2025/02/02 by Peixoto, Adriano
#Coincidence degree theory #Maximum principle #Mixed boundary conditions #Positive solution
paper · doi:10.13137/2464-8728/36849
In this work, we prove the existence of a positive solution to the second-order nonlinear problem u′′ + f(t, u, u′) = 0 with mixed boundary conditions, where f is an Lp-Carath´eodory function satisfying certain properties. Three boundary conditions are analysed. Furthermore, we also prove the existence of a positive solution to the problem u′′ + b(t)g(u) = 0, where b(t) is an L1 function and g(u) is a continuous function. The proofs of the results are based on the Mawhin’s coincidence degree.