This article considers the eigenvalue problem for the Sturm-Liouville problem including p-Laplacian (Formula Presented), where 1 < p < ∞, πp is the generalized π given by πp = 2π/ (p sin(π/p)), r ∈ C[0, πp] and λ < p − 1. Sharp Lyapunov-type inequalities, which are necessary conditions for the existence of nontrivial solutions of the above problem are presented. Results are obtained through the analysis of variational problem related to a sharp Sobolev embedding and generalized trigonometric and hyperbolic functions.
|Publication status||Published - 2020 Oct 4|
- Generalized hyperbolic functions
- Generalized trigonometric functions
- Lyapunov-type inequality
- Sharp Sobolev inequality
ASJC Scopus subject areas