Title: Partial Differential Equations and Applied Mathematics Seminar (2016.12.2)
Author: CMAC
Date: 2016-11-14 (21:42)

Partial Differential Equations and Applied Mathematics Seminar

Date/Time: Dec 2th, Fri., 2:00 ~ 3:00 PM

Location: Science Building #225 Yonsei University

Speaker: 고은경 박사

Affiliation: 울산 과학기술원

Title: Existence of multiple positive solutions for a singular p(x)-Laplacian equation


In this talk we consider the singular $p(x)$-Laplacian problem. We first prove $C^{1,\alpha}$ regularity of weak solutions of the problem by showing that weak solutions belong to some class of De Giorgi type. We also establish strong comparison principle for a singular $p(x)$-Laplacian problem. Based on these two results, we prove the existence of multiple (at least two) positive solutions for a certain range of $\lambda$ by using variational method.