Sobolev versus Hölder local minimizers and existence of multiple solutions for a singular quasilinear equation

By Jacques Giacomoni, Ian Schindler, Peter Takác. 2007

222 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/6e3f269524389ac28bb3d91c577441a2823e0cf8

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Citations in the corpus

Multiplicity of positive solutions for a singular and critical problem (2009, background): “In [10], the corresponding quasilinear and singular p-Laplacian equation is considered.”
Local "superlinearity"and "sublinearity" for the p-Laplacian (2009, background): “Note that the assumption 0 6 f ≺ g was also considered recently in a slightly different setting in [22].”
On Dirichlet problem for fractional p-Laplacian with singular non-linearity (2016, background): “multiplicity results for the Laplacian and the p-Laplacian with singular non-linearity, see [1, 11, 14, 18, 20, 23, 24].”
Nonlinear nonhomogeneous singular problems (2019, background): “Previously, such bifurcation type results have been proved by Sun, Wu & Long [41], Haitao [18], Ghergu & Rădulescu [14, 15, 16] (semilinear problems driven by the Laplacian), and by Giacomoni, Schindler & Takač [17], Papageorgiou, Rădulescu & Repovš [35], Papageorgiou & Smyrlis [36], Papageorgiou, V”
Positive solutions for nonlinear parametric singular Dirichlet problems (2018, methodology): “[7] J. Giacomoni, I. Schindler, P. Takač, Sobolev versus Hölder local minimizers and existence of multiple solutions for a singular quasilinear equation, Ann.”
Mixed local and nonlocal Sobolev inequalities with extremal and associated quasilinear singular elliptic problems (2021, unknown): “In the perturbed singular case, multiplicity results for the problem (P) have been obtained by Arcoya-Mérida [5], ArcoyaBoccardo [4] in the semilinear case; Giacomoni-Schindler-Takáč [51], Bal-Garain-Mukherjee [7, 48] in the quasilinear case and the references therein.”
Positive solutions for nonlinear Neumann problems with singular terms and convection (2020, methodology): “[7] J. Giacomoni, I. Schindler, P. Takač, Sobolev versus Hölder local minimizers and existence of multiple solutions for a singular quasilinear equation, Ann.”