Implicit elliptic equations via Krasnoselskii-Schaefer type theorems

Existence of solutions to the Dirichlet problem for implicit elliptic equations is established by using Krasnoselskii–Schaefer type theorems owed to Burton–Kirk and Gao–Li–Zhang. The nonlinearity of the equations splits into two terms: one term depending on the state, its gradient and the elliptic p...

Full description

Saved in:
Bibliographic Details
Main Author: Precup Radu
Format: Serial
Published: 2020
Series:Electronic journal of qualitative theory of differential equations : special edition 4 No. 87
Kulcsszavak:Differenciálegyenlet
doi:10.14232/ejqtde.2020.1.87

Online Access:http://acta.bibl.u-szeged.hu/73777
Description
Summary:Existence of solutions to the Dirichlet problem for implicit elliptic equations is established by using Krasnoselskii–Schaefer type theorems owed to Burton–Kirk and Gao–Li–Zhang. The nonlinearity of the equations splits into two terms: one term depending on the state, its gradient and the elliptic principal part is Lipschitz continuous, and the other one only depending on the state and its gradient has a superlinear growth and satisfies a sign condition. Correspondingly, the associated operator is a sum of a contraction with a completely continuous mapping. The solutions are found in a ball of a Lebesgue space of a sufficiently large radius established by the method of a priori bounds.
Physical Description:9
ISSN:1417-3875