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Multiple solutions for a class of quasilinear elliptic equations of p(x)-Laplacian type with nonlinear boundary conditions

Published online by Cambridge University Press:  30 March 2010

Nguyen Thanh Chung  and
Quôc-Anh Ngô
Nguyen Thanh Chung
Affiliation:
Department of Mathematics and Informatics, Quang Binh University, 312 Ly Thuong Kiet, Dong Hoi, Quang Binh, Vietnam ([email protected])
Quôc-Anh Ngô
Affiliation:
Department of Mathematics, College of Science, Vietnam National University, Hanoi, Vietnam, and Department of Mathematics, National University of Singapore, 2 Science Drive 2, 117543Singapore ([email protected])
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Abstract

Using variational methods we study the non-existence and multiplicity of non-negative solutions for a class of quasilinear elliptic equations of p(x)-Laplacian type with nonlinear boundary conditions of the form

where Ω; is a bounded domain with smooth boundary, n is the outer unit normal to ∂Ω and λ is a parameter. Furthermore, we want to emphasize that g : ∂Ω × [0,∞)→ ℝ is a continuous function that may or may not satisfy the Ambrosetti–Rabinowitz-type condition.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 140 , Issue 2 , April 2010 , pp. 259 - 272
Copyright
Copyright © Royal Society of Edinburgh 2010

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