Let N β₯ 3, 2 < p < 2 \* = 2N /(N -2), Ξ΅ > 0 and β¦ be a bounded domain with a smooth boundary ββ¦ . Our purpose in this paper is to consider the multiple existence of sign changing solutions of the problem
β¦ LIBER β¦
Sign-changing solutions of critical growth nonlinear elliptic systems
β Scribed by Zhongwei Tang
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 152 KB
- Volume
- 64
- Category
- Article
- ISSN
- 0362-546X
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β¦ Synopsis
In this paper, we are concerned with the existence of sign-changing solutions of a class of nonlinear elliptic systems with critical growth.
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Let \(\Omega\) be a smooth bounded domain of \(\mathbb{R}^{n}, n \geqslant 3\), and let \(a(x)\) and \(f(x)\) be two smooth functions defined on a neighbourhood of \(\Omega\). First we study the existence of nodal solutions for the equation \(\Delta u+a(x) u=f(x)|u|^{4 /(n-2)} u\) on \(\Omega, u=0\)