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.
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Published in Neliniini Kolyvannya, Vol. 17, No. 1, pp. 112–126, January–March, 2014.
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Sveikate, N., Sadyrbaev, F. Quasilinearization of Resonant Boundary-value Problems with Mixed Boundary Conditions. J Math Sci 205, 832–847 (2015). https://doi.org/10.1007/s10958-015-2287-7
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DOI: https://doi.org/10.1007/s10958-015-2287-7