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Solutions of singular semilinear elliptic equations with critical weighted Hardy-Sobolev exponents

100%
Du Q.-W., Tang C.-L.
Annales Polonici Mathematici
|
2014
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tom 110
|
nr 2
109-121
EN
Some solutions are obtained for a class of singular semilinear elliptic equations with critical weighted Hardy-Sobolev exponents by variational methods and some analysis techniques.
2
Content available remote

Existence of two positive solutions for a class of semilinear elliptic equations with singularity and critical exponent

81%
Liao J.-F., Liu J., Zhang P., Tang C.-L.
Annales Polonici Mathematici
|
2016
|
tom 116
|
nr 3
273-292
EN
We study the following singular elliptic equation with critical exponent ⎧$-Δu = Q(x)u^{2*-1} + λu^{-γ}$ in Ω, ⎨u > 0 in Ω, ⎩u = 0 on ∂Ω, where $Ω ⊂ ℝ^{N}$ (N≥3) is a smooth bounded domain, and λ > 0, γ ∈ (0,1) are real parameters. Under appropriate assumptions on Q, by the constrained minimizer and perturbation methods, we obtain two positive solutions for all λ > 0 small enough.
3
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Existence of three solutions for a class of (p₁,...,pₙ)-biharmonic systems with Navier boundary conditions

81%
Heidarkhani S., Tian Y., Tang C.-L.
Annales Polonici Mathematici
|
2012
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tom 104
|
nr 3
261-277
EN
We establish the existence of at least three weak solutions for the (p1,…,pₙ)-biharmonic system ⎧$Δ(|Δu_{i}|^{p−2}Δu_{i}) = λF_{u_{i}}(x,u₁,…,uₙ)$ in Ω, ⎨ ⎩$u_{i} = Δu_{i} = 0$ on ∂Ω, for 1 ≤ i ≤ n. The proof is based on a recent three critical points theorem.
4
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Nontrivial solutions for a class of superquadratic elliptic equations

81%
Li C., Ou Z.-Q., Tang C.-L.
Studia Mathematica
|
2013
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tom 214
|
nr 3
223-236
EN
Using a version of the Local Linking Theorem and the Fountain Theorem, we obtain some existence and multiplicity results for a class of superquadratic elliptic equations.
5
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On Kirchhoff type problems involving critical and singular nonlinearities

81%
Lei C.-Y., Chu C.-M., Suo H.-M., Tang C.-L.
Annales Polonici Mathematici
|
2015
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tom 114
|
nr 3
269-291
EN
In this paper, we are interested in multiple positive solutions for the Kirchhoff type problem ⎧$-(a + b∫_{Ω} |∇u|²dx)Δu = u⁵ + λ u^{q-1}/|x|^{β}$ in Ω ⎨ ⎩ u = 0 on ∂Ω, where Ω ⊂ ℝ³ is a smooth bounded domain, 0∈Ω, 1 < q < 2, λ is a positive parameter and β satisfies some inequalities. We obtain the existence of a positive ground state solution and multiple positive solutions via the Nehari manifold method.
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