Abstract
Let Ω be a bounded domain in \({\mathbb{R}^2}\) with smooth boundary. We consider the following singular and critical elliptic problem with discontinuous nonlinearity:
where \({0\leq q < 1 ,0< \alpha\leq4\pi}\) and \({\beta \in [0, 2)}\) such that \({\frac{\beta}{2} + \frac{\alpha}{4\pi} \leq 1}\) and \({{g(t - a) = \left\{\begin{array}{ll}1, t \leq a\\ 0, t > a.\end{array}\right.}}\) Under the suitable assumptions on m(x, t) we show the existence and multiplicity of solutions for maximal interval for λ.
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Sreenadh, K., Tiwari, S. Multiple positive solutions of singular and critical elliptic problem in \({\mathbb{R}^2}\) with discontinuous nonlinearities. Nonlinear Differ. Equ. Appl. 20, 1831–1850 (2013). https://doi.org/10.1007/s00030-013-0232-3
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DOI: https://doi.org/10.1007/s00030-013-0232-3