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Sobolev inequalities for the Hardy–Schrödinger operator: extremals and critical dimensions
In this survey paper, we consider variational problems involving the Hardy–Schrödinger
operator L_ γ:=-Δ-γ| x|^ 2 L γ:=-Δ-γ| x| 2 on a smooth domain Ω Ω of R^ n R n with 0 ∈ Ω 0∈ …
operator L_ γ:=-Δ-γ| x|^ 2 L γ:=-Δ-γ| x| 2 on a smooth domain Ω Ω of R^ n R n with 0 ∈ Ω 0∈ …
Solutions for semilinear elliptic equations with critical exponents and Hardy potential
D Cao, P Han - Journal of Differential Equations, 2004 - Elsevier
In this paper, we answer affirmatively an open problem (cf. Theorem 4′ in Ferrero and
Gazzola (J. Differential Equations 177 (2001) 494): Let Ω∋ 0 be an open-bounded domain …
Gazzola (J. Differential Equations 177 (2001) 494): Let Ω∋ 0 be an open-bounded domain …
Elliptic equations with multi-singular inverse-square potentials and critical nonlinearity
This article deals with a class of nonlinear elliptic equations involving a critical power-
nonlinearity as well as a potential featuring multiple inverse square singularities. We show …
nonlinearity as well as a potential featuring multiple inverse square singularities. We show …
Ground state solutions for Hamiltonian elliptic system with inverse square potential
J Zhang, W Zhang, X Tang - Discrete and Continuous Dynamical …, 2017 - aimsciences.org
$\left\{\begin {array}{ll}-\Delta u+\vec {b}(x)\cdot\nabla u+ V (x) u-\frac {\mu}{| x|^{2}} v= H_
{v}(x, u, v)\\-\Delta v-\vec {b}(x)\cdot\nabla v+ V (x) v-\frac {\mu}{| x|^{2}} u= H_ {u}(x, u, v)\\\end …
{v}(x, u, v)\\-\Delta v-\vec {b}(x)\cdot\nabla v+ V (x) v-\frac {\mu}{| x|^{2}} u= H_ {u}(x, u, v)\\\end …
[کتاب][B] Sign-changing critical point theory
W Zou - 2008 - books.google.com
Many nonlinear problems in physics, engineering, biology and social sciences can be
reduced to finding critical points of functionals. While minimax and Morse theories provide …
reduced to finding critical points of functionals. While minimax and Morse theories provide …
On Schrödinger operators with multipolar inverse-square potentials
Positivity, essential self-adjointness, and spectral properties of a class of Schrödinger
operators with multipolar inverse-square potentials are discussed. In particular a necessary …
operators with multipolar inverse-square potentials are discussed. In particular a necessary …
Solutions to critical elliptic equations with multi-singular inverse square potentials
D Cao, P Han - Journal of Differential Equations, 2006 - Elsevier
Let Ω be an open-bounded domain in RN (N⩾ 3) with smooth boundary∂ Ω. We are
concerned with the multi-singular critical elliptic problem where μi∈ R, 2*= 2NN-2, ai∈ Ω …
concerned with the multi-singular critical elliptic problem where μi∈ R, 2*= 2NN-2, ai∈ Ω …
A Berestycki–Lions theorem revisited
In 1983, Berestycki and Lions [Nonlinear scalar field equations I. Existence of a ground
state, Arch. Ration. Mech. Anal. 82 (1983) 313–346] studied the following elliptic problem …
state, Arch. Ration. Mech. Anal. 82 (1983) 313–346] studied the following elliptic problem …
Infinitely many solutions for an elliptic problem involving critical Sobolev growth and Hardy potential
D Cao, S Yan - Calculus of Variations and Partial Differential …, 2010 - Springer
In this paper, we will prove the existence of infinitely many solutions for the following elliptic
problem with critical Sobolev growth and a Hardy potential:-Δ u-μ| x|^ 2 u=| u|^ 2^ ∗-2 u+ …
problem with critical Sobolev growth and a Hardy potential:-Δ u-μ| x|^ 2 u=| u|^ 2^ ∗-2 u+ …
Standing waves for nonlinear Schrödinger equations involving critical growth
We consider the following singularly perturbed nonlinear elliptic problem: where and is the
nonlinearity of critical growth. In this paper, we construct a solution of the above problem …
nonlinearity of critical growth. In this paper, we construct a solution of the above problem …