Lane–Emden systems with negative exponents
By Marius Ghergu. 2010
78 citations recorded by the source corpus.
We study the elliptic system {−Δu=u−pv−qin Ω,−Δv=u−rv−sin Ω,u=v=0on ∂Ω, in a bounded domain Ω⊂RN (N⩾1) with a smooth boundary, p,s⩾0 and q,r>0. We investigate the existence, non-existence, and uniqueness of C2(Ω)∩C(Ω¯) solutions in terms of p, q, r and s. A necessary and sufficient condition for the C1-regularity of solutions up to the boundary is also obtained.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/3764c227a7a82909dbd1a72a79fb62aa57a84993
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In Applied Mathematics
In Computational Theory and Mathematics
Citations in the corpus
- On Very Weak Positive Solutions to Some Semilinear Elliptic Problems With Simultaneous Singular Nonlinear and Spatial Dependence Terms (2011, background): “Concerning non-existence results, it was shown by Ghergu in [13] that for a > 0 and b > 0 such that b ≥ 2, there is no positive solution to (1.”