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Ground states for a nonhomogeneous elliptic system involving Hardy–Sobolev critical exponents

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0 Published in 2017 at "Mathematische Nachrichten"

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

Multiplicity of solutions for a nonlocal nonhomogeneous elliptic equation with critical exponential growth

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0 Published in 2019 at "Journal of Mathematical Analysis and Applications"

DOI: 10.1016/j.jmaa.2019.03.039

Abstract: Abstract In this paper we are interested in the following nonlocal nonhomogeneous elliptic equation in R 2 , − Δ u + V ( x ) u = ( 1 | x | μ ⁎… read more here.

Keywords: multiplicity solutions; nonhomogeneous elliptic; exponential growth; elliptic equation ... See more keywords

Nontrivial weak solutions for nonlocal nonhomogeneous elliptic problems

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0 Published in 2020 at "Applicable Analysis"

DOI: 10.1080/00036811.2020.1778674

Abstract: This article concerns the following class of nonlocal nonhomogeneous elliptic problems: − ∫ Ω g ( x , u ) d x β div ⁡ ( a ( x ) ∇ u ) = (… read more here.

Keywords: solutions nonlocal; weak solutions; nontrivial weak; nonlocal nonhomogeneous ... See more keywords

Deep Learning Nonhomogeneous Elliptic Interface Problems by Soft Constraint Physics-Informed Neural Networks

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2 Published in 2023 at "Mathematics"

DOI: 10.3390/math11081843

Abstract: It is a great challenge to solve nonhomogeneous elliptic interface problems, because the interface divides the computational domain into two disjoint parts, and the solution may change dramatically across the interface. A soft constraint physics-informed… read more here.

Keywords: informed neural; neural networks; physics; interface ... See more keywords