MATEMATIČKI VESNIK МАТЕМАТИЧКИ ВЕСНИК

 SHARP ASYMPTOTIC ANALYSIS OF POSITIVE SOLUTIONS OF A COMBINED STURM-LIOUVILLE PROBLEM S. Belkahla, Z. Zine El Abidine AbstractIn this work, we investigate a class of nonlinear combined Sturm-Liouville problems with zero Dirichlet boundary conditions. Using the Karamata regular variation theory and the Sch{a}uder fixed point theorem, we prove the existence of a unique positive solution satisfying a precise asymptotic behavior where a competition between singular and non singular terms in the nonlinearity appears. Keywords: Asymptotic analysis; Sturm-Liouville equation; Dirichlet problem; Green function; Karamata class; Schäuder's fixed point theorem. MSC: 26A12, 34B16, 34B18, 34B27 Pages:  58$-$70 Volume  75 ,  Issue  1 ,  2023

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