Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents

By Nassif Ghoussoub, C. Yuan. 2000

552 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9c2745fd472227399688a02d84d8d54118dac639

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In Applied Mathematics

1. Nguyen Huong Lam
2. G. Lu
3. Shuangjie Peng
4. Daomin Cao
5. Zhi-Qiang Wang
6. I. Peral
7. Jiabao Su
8. Nassif Ghoussoub

In Mathematical Physics

1. Shuangjie Peng
2. Nguyen Huong Lam
3. G. Lu
4. Zhi-Qiang Wang
5. Jiabao Su
6. Nassif Ghoussoub
7. I. Peral
8. Daomin Cao

Citations in the corpus

• The critical hyperbola for a Hamiltonian elliptic system with weights (2008, result): “Results of existence, non-existence and multiplicity for elliptic equations involving weights could be found, among other papers, in [1–5,9,10,25 ]a nd [ 27 ].”
• Sharp Constants and Optimizers for a Class of Caffarelli–Kohn–Nirenberg Inequalities (2015, background): “[27] Ghoussoub, N.; Yuan, C. Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents.”
• Existence and non-existence of solutions to elliptic equations related to the Caffarelli–Kohn–Nirenberg inequalities (2007, unknown): “More results can be found in [7, 15, 18, 19, 20, 22].”
• Concentration estimates for Emden-Fowler equations with boundary singularities and critical growth (2005, background): “More precisely, we need the principal curvatures of ∂Ω at 0 to be non-positive but not all vanishing.”
• Multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents (2003, unknown): “The Theorem B extends the multiplicity of solutions in [14] to the case p 0 is a consequence of a recent result due to Ghoussoub and Yuan [ 15 ].”
• Nonlocal problems with critical Hardy nonlinearity (2017, background): “Even if not needed, proceeding as in [10] it can be proved that actually c1,ρ → c1,0.”
• A note on the sign-changing solutions to elliptic problems with critical Sobolev and Hardy terms $ (2003, methodology): “In fact, a subsequence of unn converges strongly to u in H 1 0 ðOÞ: To see this, notice c2;n-c2;0 (similar to that in [9]), it is easy to verify that funng is actually a Palais-Smale sequence for J0 at level c2;0: So by the fact that limn-N c1;nn 1⁄4 c1:0 and Lemma 2.”