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Existence of solution for quasilinear equations involving local conditions
Published online by Cambridge University Press: 17 September 2019
Abstract
In this paper, we study the existence of weak solutions of the quasilinear equation
where a : ℝ → [0, ∞) is C1 and a nonincreasing continuous function near the origin, the nonlinear term f : Ω × ℝ → ℝ is a Carathéodory function verifying certain superlinear conditions only at zero, and λ is a positive parameter. The existence of the solution relies on C1-estimates and variational arguments.
\begin{cases} -{\rm div} (a(\vert \nabla u \vert ^2)\nabla u)=\lambda f(x,u) &{\rm in} \ \Omega,\\ u=0 &{\rm on} \ \partial\Omega, \end{cases}
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 6 , December 2020 , pp. 3074 - 3086
- Copyright
- Copyright © 2019 The Royal Society of Edinburgh
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