Multiple positive solutions for singular elliptic problems involving concave-convex nonlinearities and sign-changing potential

Hong-Ying Li (), Yang Pu () and Jia-Feng Liao ()
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Hong-Ying Li: China West Normal University
Yang Pu: China West Normal University
Jia-Feng Liao: China West Normal University

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 2, 611-630

Abstract: Abstract In this paper, we are interested in considering the following singular elliptic problem with concaveconvex nonlinearities $$\left\{ {\begin{array}{*{20}{l}} { - \Delta u - \frac{\mu }{{|x{|^2}}}u = f(x)|u{|^{p - 2}}u + g(x)|u{|^{q - 2}}u,}&{in\;\;\Omega \backslash \{ 0\} ,} \\ {u = 0,}&{on\;\;2\Omega ,} \end{array}} \right.$${-Δu-µ|x|2u=f(x)|u|p−2u+g(x)|u|q-2u,inΩ\{0},u=0,on2Ω, where Ω ⊂ ℝN(N ≥ 3) is a smooth bounded domain with 0 ∈ Ω, $$0

Keywords: Singular elliptic problem; concave-convex nonlinearities; ground state solution; Nehari method; 35J20; 35J61; 35D30 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0420-x

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