Existence and local boundedness of solutions of a -Laplacian problem. Issue 4 (12th March 2019)

• Record Type: Journal Article
• Authors: Arriagada, Waldo; Huentutripay, Jorge
• Is Part Of: Applicable analysis. Volume 98:Issue 4(2019)
• Page Start: 667
• Page End: 681
• Publication Date: 2019-03-12
• Subjects: Orlicz-Sobolev space -- eigenvalue problem -- ϕ-Laplacian -- local boundedness; 35P30 -- 35J20 -- 46E30; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1404581
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we consider theϕ -Laplacian equation- div ϕ ( | ∇ u | ) ∇ u / | ∇ u | = λ g ( · ) ϕ ( u ) in R N whereϕ is an odd increasing homeomorphism fromR ontoR which is not necessarily differentiable. The termλ is a suitable parameter and g is measurable. We prove that nontrivial and nonnegative weak solutions of this equation exist. The problem on the local boundedness of the solutions is also treated. Mild restrictions are imposed on g andϕ .