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Multiple solutions of boundary value problems on time scales for φ-laplacian operator

Amster Pablo, Kuna Mariel Paula, Santos Dionicio Pastor

Opuscula Mathematica

2020

Vol. 40, no. 4

405--425

We establish the existence and multiplicity of solutions for some boundary value problems on time scales with a y-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.

Existence theorems of nonlinear asymptotic BVP for a homeomorphism

Szymańska-Dębowska K.

Opuscula Mathematica

2016

Vol. 36, no. 3

399--407

In this work, we are concerned with the existence of solutions for the following φ -Laplacian boundary value problem on the half-line [formula] where [formula] is continuous. The results are proved using the properties of the Leray-Schauder topological degree.