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Applicable Analysis
An International Journal
Volume 98, 2019 - Issue 4
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Articles

Existence and local boundedness of solutions of a -Laplacian problem

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Pages 667-681 | Received 23 Nov 2016, Accepted 09 Nov 2017, Published online: 22 Nov 2017
 

ABSTRACT

In this paper, we consider the ϕ-Laplacian equation -divϕ(|u|)u/|u|=λg(·)ϕ(u)inRN

where ϕ is an odd increasing homeomorphism from R onto R which is not necessarily differentiable. The term λ 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 and ϕ.

AMS SUBJECT CLASSIFICATIONS:

Notes

No potential conflict of interest was reported by the authors.

1 Hypothesis (H2) generalizes the natural condition gLN/p(RN)L(RN) imposed on the right-hand side of the eigenvalue differential problem considered in [Citation10]. Indeed, in that reference the authors treat the classical case of the p-Laplacian Δpu=div(|u|p-2u) for which pΦ=qΦ=p and the quantity qΦ/(qΦ-pΦ)=N/p.

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