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.

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  • Pablo Amster (corresponding author)
  • ORCID iD 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
  • ORCID iD 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
  • ORCID iD 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.
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Cite this article as:
Pablo Amster, Mariel Paula Kuna, Dionicio Pastor Santos, Multiple solutions of boundary value problems on time scales for a φ-Laplacian operator, Opuscula Math. 40, no. 4 (2020), 405-425, https://doi.org/10.7494/OpMath.2020.40.4.405

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