We consider resonant problems of the form (i) x″ + p(t)x′ + q(t)x = f(t, x, x′), (ii) x′(0) = 0, x(T) = 0, where p, q, and f are continuous functions, and a homogeneous problem (iii) x″ + p(t)x′ + q(t)x = 0 with the boundary conditions (ii), which has a nontrivial solution. The problem is studied by modifying the linear part and applying the procedure of quasilinearization to the modified problem.
Cauchy Problem Linear Part Trivial Solution Multiple Solution Homogeneous Problem
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