Opuscula Math. 40, no. 4 (2020), 405-425
https://doi.org/10.7494/OpMath.2020.40.4.405
Opuscula Mathematica
Multiple solutions of boundary value problems on time scales for a φ-Laplacian operator
Pablo Amster
Mariel Paula Kuna
Dionicio Pastor Santos
Abstract. We establish the existence and multiplicity of solutions for some boundary value problems on time scales with a \(\varphi\)-Laplacian operator. For this purpose, we employ the concept of lower and upper solutions and the Leray-Schauder degree. The results extend and improve known results for analogous problems with discrete \(p\)-Laplacian as well as those for boundary value problems on time scales.
Keywords: dynamic equations on time scales, nonlinear boundary value problems, upper and lower solutions, Leray-Schauder degree, multiple solutions.
Mathematics Subject Classification: 34N05, 34K10, 47H11.
- Pablo Amster (corresponding author)
https://orcid.org/0000-0003-2829-7072- Universidad de Buenos Aires & IMAS-CONICET, Facultad de Ciencias Exactas y Naturales, Departamento de Matemática, Ciudad Universitaria, Pabellón I, Buenos Aires (1428), Argentina
- Mariel Paula Kuna
- https://orcid.org/0000-0001-6466-973X
- Universidad de Buenos Aires & IMAS-CONICET, Facultad de Ciencias Exactas y Naturales, Departamento de Matemática, Ciudad Universitaria, Pabellón I, Buenos Aires (1428), Argentina
- Dionicio Pastor Santos
- https://orcid.org/0000-0001-5574-6254
- Universidad de Buenos Aires & IMAS-CONICET, Facultad de Ciencias Exactas y Naturales, Departamento de Matemática, Ciudad Universitaria, Pabellón I, Buenos Aires (1428), Argentina
- Communicated by Petr Stehlík.
- Received: 2020-01-31.
- Revised: 2020-05-06.
- Accepted: 2020-05-11.
- Published online: 2020-07-09.
