Existence and multiplicity of solutions for critical elliptic equations with multi-polar potentials in symmetric domains
β Scribed by Qianqiao Guo; Junqiang Han; Pengcheng Niu
- Book ID
- 116761243
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 378 KB
- Volume
- 75
- Category
- Article
- ISSN
- 0362-546X
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π 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 \(\Omega, u=0\)
In this paper, we study the decomposition of the filtration of the Nehari manifold via the variation of domain shape. Furthermore, we use this result to prove that the semilinear elliptic equation in the multi-bump domain (r) has multiple positive solutions and we can find at least one ground state