Multiplicity of solutions for a Dirichlet problem with a strongly singular nonlinearity

By David Arcoya, Lourdes Moreno-Mérida. 2014

88 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/74f66181c9ebc343ef41f359d90f4307bfe0fae9

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Semilinear problems for the fractional laplacian with a singular nonlinearity (2015, background): “L2/ D 8̂̂<̂ :̂ u D u C u in ; u > 0 in ; u D 0 in @; where , p and are positive numbers (see, among other papers, [3, 4, 8, 12, 14, 21, 35] for an extensive analysis of this kind of problems).”
Finite and infinite energy solutions of singular elliptic problems: Existence and uniqueness (2016, background): “In [3] the authors prove the existence of a solution u ∈ H1 0 (Ω) if 1 < γ < 3m−1 m+1 providedf is strictly bounded away from zero.”
On singular elliptic equations with measure sources (2015, background): “1) has been considered in [8] again in the homogeneous case μ ≡ 0 (see also [6, 3] for further improvements).”
Combined effects in mixed local–nonlocal stationary problems (2021, unknown): “     u ∈ W 1, Nr(1+γ) N−r(1−γ) 0 (Ω) if 0 < γ < 1 and f ∈ L (Ω) with r ∈ [1, (2/(1− γ))), u ∈ H(1) 0 (Ω) if 0 < γ < 1 and f ∈ L (Ω) with r = (2/(1− γ)), u ∈ H(1) 0 (Ω) if γ = 1 and f ∈ L (1)(Ω), u 1+γ 2 ∈ H(1) 0 (Ω) if γ > 1 and f ∈ L (1)(Ω), Extending the work of [16], Arcoya and Mérida in [5]”
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.”