Opuscula Math. 40, no. 4 (2020), 405-425
Multiple solutions of boundary value problems on time scales for a φ-Laplacian operator
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.
- Communicated by Petr Stehlík.
- Received: 2020-01-31.
- Revised: 2020-05-06.
- Accepted: 2020-05-11.
- Published online: 2020-07-09.