Some nonlinear boundary value problems of mixed type on a half line for quasilinear second-order ordinary differential systems

Jean Mawhin; Katarzyna Szymanska-Debowska

doi:10.4171/zaa/1832

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Some nonlinear boundary value problems of mixed type on a half line for quasilinear second-order ordinary differential systems

Jean Mawhin
Université Catholique de Louvain, Louvain-la-Neuve, Belgium
Katarzyna Szymanska-Debowska
Lodz University of Technology, Poland

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Abstract

Using Leray–Schauder degree, the existence of solutions for quasilinear systems of the form $(q (t) Φ (x^{'}))^{'} = f (t, x, x^{'})$ , with nonlinear boundary conditions of mixed type

F (x (0), G (x), H (x^{'})) = 0, x^{'} (\infty) = 0,

is proved for various classes of $Φ$ when $F$ and $f$ satisfy suitable sign conditions.

Cite this article

Jean Mawhin, Katarzyna Szymanska-Debowska, Some nonlinear boundary value problems of mixed type on a half line for quasilinear second-order ordinary differential systems. Z. Anal. Anwend. (2026), published online first

DOI 10.4171/ZAA/1832