Nodal solutions of elliptic equations with critical Sobolev exponents
β Scribed by F.V Atkinson; H Brezis; L.A Peletier
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 686 KB
- Volume
- 85
- Category
- Article
- ISSN
- 0022-0396
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Let β R N be a smooth bounded domain such that 0 β ; N ΒΏ 3; 0 6 s Β‘ 2; 2 \* (s Via the variational methods, We prove the existence of sign-changing solutions for the singular critical problem -u -u=|x| 2 = |u| 2 \* (s)-2 =|x| s u + |u| r-2 u with Dirichlet boundary condition on for suitable po
The existence and multiplicity of positive solutions are obtained for a class of semilinear elliptic equations with critical weighted Hardy-Sobolev exponents and the concaveconvex nonlinearity by variational methods and some analysis techniques.
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 \(\Omega, u=0\)