Abstract

In 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

DOI: 10.57016/MV-XFOQ5120

Pages:  58$-$70     

Volume  75 ,  Issue  1 ,  2023