Combined Effects of Singular and Superlinear Nonlinearities in Some Singular Boundary Value Problems

By Yijing Sun, Shaoping Wu, Y. Long. 2001

208 citations recorded by the source corpus.

Abstract This paper deals with a class of singular semilinear elliptic Dirichlet boundary value problems where the combined effects of a superlinear and a singular term allow us to establish some existence and multiplicity results.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/7188ae8b9ce83e5720b093f9b38548a2c23cccca

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In Applied Mathematics

In Numerical Analysis

Citations in the corpus

Existence and multiplicity of positive solutions for singular quasilinear problems (2006, methodology): “In the superlinear subcritical case 1 < β < 2∗− 1 with small λ, Coclite and Palmieri [5] obtained a solution when a = 1 and Sun, Wu, and Long [19] obtained two solutions using the Ekeland’s variational principle for more general a’s.”
A bifurcation-type theorem for singular nonlinear elliptic equations (2015, unknown): “For singular equations, such problems were studied by Coclite-Palmieri [4], Crandall-Rabinowitz-Tartar [5], Hirano-Saccon-Shioji [11], LairShaker [14], Lazer-MacKenna [15], Sun-Wu-Long [21] for p = 2 (semilinear equations) and Giacomoni-Schindler-Takac [8], Perera-Zhang [19] for p = 2 (nonlinear equ”
Multiplicity of positive solutions for a singular and critical problem (2009, methodology): “Assuming 0 < δ < 1, [5] apply variational arguments based on Nehari’s method to show the existence of at least two solutions for q > 1 subcritical: q < ∞ if N = 1 or 2, and q < 2 − 1 if N ≥ 3.”
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].”
Existence of solutions for singular double phase problems via the Nehari manifold method (2021, methodology): “For related works dealing with certain types of double phase problems we refer to the works of Alves-Santos-Silva [1], Bahrouni-Rădulescu-Winkert [2], BarlettaTornatore [3], Biagi-Esposito-Vecchi [8], Lei [33], Papageorgiou-Rădulescu-Repovš [46], Rădulescu [53], Sun-Wu-Long [56], Wang-Zhao-Zhao [58]”
Sobolev versus Hölder local minimizers and existence of multiple solutions for a singular quasilinear equation (2007, methodology): “Assuming 0 < δ < 1, Yijing, Shaoping, and Yiming [44] apply variational arguments based on Nehari’s method [35] to show the existence of at least two solutions for q > 1 subcritical: q < ∞ if N = 1 or 2, and q < 2∗ − 1 = N+2 N−2 if N ≥ 3.”