Nonlinear degenerate elliptic equation with Hardy potential and critical parameter
β Scribed by Yao-tian Shen; Zhi-hui Chen
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 345 KB
- Volume
- 69
- Category
- Article
- ISSN
- 0362-546X
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π SIMILAR VOLUMES
## Abstract In a previous work [6], we got an exact local behavior to the positive solutions of an elliptic equation. With the help of this exact local behavior, we obtain in this paper the existence of solutions of an equation with HardyβSobolev critical growth and singular term by using variation
Some existence and multiplicity results are obtained for solutions of semilinear elliptic equations with Hardy terms, Hardy-Sobolev critical exponents and superlinear nonlinearity by the 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 \(\Omega, u=0\)