Abstract
In this paper, we are interested in considering the following singular elliptic problem with concaveconvex nonlinearities
where Ω ⊂ ℝN(N ≥ 3) is a smooth bounded domain with 0 ∈ Ω, \(0 < \mu < \bar\mu = \frac{{{{(N - 2)}^2}}}{4}\), 1 < q < 2 < p < 2* and \(2* = \frac{{2N}}{{N - 2}}\) is the Sobolev critical exponent, the coefficient functions f, g may change sign on Ω. By the Nehari method, we obtain two solutions, and one of them is a ground state solution. Under some stronger conditions, we point that the two solutions are positive solutions by the strong maximum principle.
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Acknowledgement
The authors would like to thank the anonymous referees and the handling editor for their careful reading. The paper is supported by the Scientific Research Fund of Sichuan Provincial Education Department (18ZA0471), the Meritocracy Research Funds of China West Normal University (17YC383), the Fundamental Research Funds of China West Normal University (17E089, 18B015, 18D052) and the Innovation Team Research Funds of China West Normal University (CXTD2018-8).
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The paper is supported by the Scientific Research Fund of Sichuan Provincial Education Department(18ZA0471), the Meritocracy Research Funds of ChinaWest Normal University (17YC383), the Fundamental Research Funds of ChinaWest Normal University (17E089, 18B015, 18D052) and the Innovation Team Research Funds of ChinaWest Normal University (CXTD2018-8).
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Li, HY., Pu, Y. & Liao, JF. Multiple positive solutions for singular elliptic problems involving concave-convex nonlinearities and sign-changing potential. Indian J Pure Appl Math 51, 611–630 (2020). https://doi.org/10.1007/s13226-020-0420-x
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DOI: https://doi.org/10.1007/s13226-020-0420-x