Ground states for a nonhomogeneous elliptic system involving Hardy–Sobolev critical exponents
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DOI: 10.1002/mana.201500348
Abstract: This paper studies the following nonhomogeneous elliptic system involving Hardy–Sobolev critical exponents Δu+λ1up−1|x|s+μ1u2*(s1)−1|x|s1+αγ2*(s2)uα−1vβ|x|s2=0inΩ,Δv+λ2vp−1|x|s+μ2v2*(s1)−1|x|s1+βγ2*(s2)uαvβ−1|x|s2=0inΩ,u≥0,v≥0inΩ,u=0,v=0on∂Ω, where λ1,λ2,μ1,μ2,γ>0,2 1,α+β=2*(s2), Ω is a C1 open bounded domain in RN containing the origin, and N≥4. The existence result of positive… read more here.
Keywords: elliptic system; system involving; sobolev critical; hardy sobolev ... See more keywords
Elliptic System With Sublinear Signal Production in Dimension 2
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DOI: 10.1002/mma.70140
Abstract: We consider the nonlinear elliptic system u∈W01,q(Ω):−div(M(x)∇u)+u=−div(uM(x)∇ψ)+f(x),ψ∈W01,2(Ω):−div(M(x)∇ψ)=Φ(u),$$ {\displaystyle \begin{array}{ll}u\in {W}_0^{1,q}\left(\Omega \right):& -\operatorname{div}\left(M(x)\nabla u\right)+u=-\operatorname{div}\left(u\kern0.3em M(x)\kern0.3em \nabla \psi \right)+f(x),\\ {}\psi \in {W}_0^{1,2}\left(\Omega \right):& -\operatorname{div}\left(M(x)\nabla \psi \right)=\Phi (u),\end{array}} $$ where Ω$$ \Omega $$ is a bounded, open subset… read more here.
Keywords: amp; amp x0005e; right amp; div ... See more keywords
The first eigenvalue and eigenfunction of a nonlinear elliptic system
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DOI: 10.1016/j.apnum.2019.06.004
Abstract: In this paper, we study the first eigenvalue of a nonlinear elliptic system involving $p$-Laplacian as the differential operator. The principal eigenvalue of the system and the corresponding eigenfunction are investigated both analytically and numerically.… read more here.
Keywords: elliptic system; system; first eigenvalue; eigenvalue eigenfunction ... See more keywords
A free boundary problem for an elliptic system
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DOI: 10.1016/j.jde.2021.02.050
Abstract: Abstract We study solutions and the free boundary ∂ { | u | > 0 } of the sublinear system Δ u = λ + ( x ) | u + | q − 1… read more here.
Keywords: elliptic system; system; problem elliptic; free boundary ... See more keywords
Global existence and eventual smoothness in a 2-D parabolic-elliptic system arising from ion transport networks
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DOI: 10.1016/j.jde.2021.09.040
Abstract: Abstract The aim of this paper is to investigate a parabolic-elliptic system, which was proposed by Albi et al (2016) to describe the evolution of ion transport networks. Our first result asserts that the corresponding… read more here.
Keywords: ion transport; transport networks; elliptic system; parabolic elliptic ... See more keywords
Existence of ground state solutions to Hamiltonian elliptic system with potentials
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DOI: 10.1016/s0252-9602(18)30859-2
Abstract: Abstract In this paper, we investigate nonlinear Hamiltonian elliptic system { ( - Δ ) u = b → ( x ) ⋅ ∇ u + ( V ( x ) + τ ) u… read more here.
Keywords: hamiltonian elliptic; elliptic system; state solutions; ground state ... See more keywords
Nonclassical problem with integral boundary conditions for elliptic system
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DOI: 10.1080/17476933.2017.1351438
Abstract: Abstract In the present paper, a mixed nonclassical problem for multidimensional second-order elliptic system with Dirichlet and nonlocal integral boundary conditions is considered. Since Lax-Milgram theorem cannot be applied straightforwardly for such a nonlocal problem,… read more here.
Keywords: boundary conditions; integral boundary; nonclassical problem; elliptic system ... See more keywords
A nonlocal elliptic system with nonlinear singular terms
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DOI: 10.1080/17476933.2024.2382791
Abstract: In this work we deal with the nonlocal elliptic system: \[ \it{(S)} \begin{cases} (-\Delta)^{s_1} u = \theta\frac{v^q}{u^{1-\theta}} & {\rm in}\ \Omega , \\ (-\Delta)^{s_2} v = qv^{q-1}u^\theta & {\rm in}\ \Omega , \\ u =v… read more here.
Keywords: system; singular terms; nonlocal elliptic; system nonlinear ... See more keywords
Semi-classical states for elliptic system near saddle points of potentials
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DOI: 10.1088/1361-6544/acd045
Abstract: In this paper, we study the following Hamiltonian elliptic system −ε2Δu+u=Hv(x,u,v) in RN,−ε2Δv+v=Hu(x,u,v) in RN,u(x)→0, v(x)→0 as |x|→∞, where ɛ > 0 is a small parameter, H is a super-quadratic sub-critical Hamiltonian. Our investigation focuses on the cases that H(x,u,v)=12K(x)(u2+v2)+F(u,v) and H(x,u,v)=K(x)F(u,v) , where… read more here.
Keywords: classical states; states elliptic; saddle points; elliptic system ... See more keywords
The Numbers of Positive Solutions by the Lusternik-Schnirelmann Category for a Quasilinear Elliptic System Critical with Hardy Terms
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DOI: 10.1155/2019/4829861
Abstract: In this paper, we study the quasilinear elliptic system with Sobolev critical exponent involving both concave-convex and Hardy terms in bounded domains. By employing the technique introduced by Benci and Cerami (1991), we obtain at… read more here.
Keywords: numbers positive; hardy terms; positive solutions; elliptic system ... See more keywords
Positive symmetric results for a weighted quasilinear elliptic system with multiple critical exponents in RN$\mathbb{R}^{N}$
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DOI: 10.1186/s13661-017-0758-0
Abstract: This work focuses on the symmetric solutions for a weighted quasilinear elliptic system involving multiple critical exponents in RN$\mathbb{R}^{N}$. Based upon the Caffarelli-Kohn-Nirenberg inequality and the symmetric criticality principle due to Palais, we prove a… read more here.
Keywords: weighted quasilinear; exponents mathbb; multiple critical; critical exponents ... See more keywords