Multiplicity and asymptotic behavior of positive solutions for a singular semilinear elliptic problem

By Hai-tao Yang. 2003

204 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/814ced996fbc5d2637e45bb120891e29d33d3321

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Nonlinear nonhomogeneous singular problems (2019, background): “Primary: 35J20. Secondary: 35J75, 35J92, 35P30. 1 2 N.S. PAPAGEORGIOU, V.D. RADULESCU, AND D.D. REPOV˘ ˇS Previously, such bifurcation type results have been proved by Sun, Wu & Long [41], Haitao [18], Ghergu & Ra˘dulescu [14, 15, 16] (semilinear problems driven by the Laplacian), and by Gia”
Lane-Emden-Fowler equations with convection and singular potential (2007, background): “Such singular boundary value problems arise in the context of chemical heterogeneous catalysts and chemical catalyst kinetics, in the theory of heat conduction in electrically conducting materials, singular minimal surfaces, as well as in the study of non-Newtonian fluids or boundary layer phenomena”
Multi-parameter bifurcation and asymptotics for the singular Lane–Emden–Fowler equation with a convection term (2005, background): “In the case f(x, u) = uq, g(u) = u−γ , 0 < γ < 1 N and 1 < q < N+2 N−2 , we learn from [23] that problem (1.”
Singular phenomena in nonlinear elliptic problems. From blow-up boundary solutions to equations with singular nonlinearities (2006, background): “Nonlinear elliptic equation, singularity, boundary blow-up, bifurcation, asymptotic anal- ysis, maximum principle, Karamata regular variation theory.”
Sobolev versus Hölder local minimizers and existence of multiple solutions for a singular quasilinear equation (2007, methodology): “The critical case q = 2∗ − 1 and N ≥ 3 was settled almost simultaneously in Haitao [29] and Hirano, Saccon, and Shioji [31] by two different methods: Perron’s method and Nehari’s method, respectively.”
Multiplicity of positive solutions for a singular and critical problem (2009, methodology): “As in [6], we argue by contradiction.”
Brezis–Nirenberg type theorems and multiplicity of positive solutions for a singular elliptic problem (2008, background): “1) were recently studied by Sun, Wu and Long [24], Haitao [14] and the authors [16].”