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
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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