In this paper, we consider the semilinear elliptic equation For p=2NÂ(N&2), we show that there exists a positive constant +\\*>0 such that (V) + possesses at least one solution if + # (0, +\\*) and no solutions if +>+\\*. Furthermore, (V) + possesses a unique solution when +=+\\*, and at least two s
Existence and non-existence of radial solutions for elliptic equations with critical exponent in ℝ2
✍ Scribed by D. G. De Figueiredo; B. Ruf
- Publisher
- John Wiley and Sons
- Year
- 1995
- Tongue
- English
- Weight
- 605 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0010-3640
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📜 SIMILAR VOLUMES
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 \(\Omega, u=0\)
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## Abstract In this paper, we prove the existence and uniqueness of a global solution for 2‐D micropolar fluid equation with periodic boundary conditions. Then we restrict ourselves to the autonomous case and show the existence of a global attractor. Copyright © 2006 John Wiley & Sons, Ltd.