Solutions for semilinear elliptic equations with critical exponents and Hardy potential

By Daomin Cao, Pigong Han. 2004

163 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/06d4c2b23d34a31571e722af5af6bfa2f990cff8

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Asymptotic behaviors of solutions to quasilinear elliptic equations with critical Sobolev growth and Hardy potential (2015, methodology): “s both a weak subsolution and a weak supersolution. Equation (1.1) and its variants have been extensively studied in the literature. For the existence of solutions to equation (1.1), we refer to e.g. [3, 4, 7, 8, 9, 10, 11, 16, 17, 19, 20, 26]. For the uniqueness of solutions to equation (1.1), we r”
Solutions to critical elliptic equations with multi-singular inverse square potentials (2006, unknown): “For any 0 ̄, ∫ ( |∇ua , |2 − (ua , ) 2 |x − a|2 ) dx = S N 2 + O ( 2 √ ̄− ) , (3.10) D. Cao, P. Han / J. Differential Equations 224 (2006) 332–372 355∫ |ua , |2 ∗ dx = S N 2 + O ( 2N N−2 √ ̄− ) (3.11) and for any ∈ RN\{0}, ∫ |u0 , |2 |x + |2 dx = ⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩ 2 | |2 ∫ RN U2 ,0(x) dx + o( 2) if ”
Infinitely many solutions for an elliptic problem involving critical Sobolev growth and Hardy potential (2010, unknown): “solution of (1.1) is singular at x = 0i fμ � 0( see [ 8 ,9]).”
Existence and non-existence of solutions to elliptic equations related to the Caffarelli–Kohn–Nirenberg inequalities (2007, background): “5)  −∆u = μ u |x|2 + |x|βup(β)−1 + f(x, u), x ∈ Ω, u(x) = 0, x ∈ ∂Ω, where 0 ≤ μ < (N − 2)(2)/4, p(β) = 2(N + β)/(N − 2), −2 < β ≤ 0, f(x, u) is a subcritical perturbation; see [1, 8, 10, 11, 15, 19, 20, 23, 24, 25, 26] et al.”