Abstract
In this paper, we study the existence of positive solutions for the quasilinear elliptic singular problem
where \({c,\lambda >0}\), \({\gamma \in (0,1)}\), f is strictly increasing and derivable in \({[0,\infty)}\) with \({f(0)>0}\). We show that there exists \({\lambda^*>0}\) such that \({(0,\lambda^*]}\) is the maximal set of values such there exists solution. In addition, we prove that for \({\lambda<\lambda^*}\) there exists minimal and bounded solutions. Moreover, we give sufficient conditions for existence and regularity of solutions for \({\lambda=\lambda^*}\).
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Research supported by MINECO Grant MTM2015-68210-P (Spain) and Junta de Andalucía FQM-116 (Spain). Dedicated to Antonio Molino, a great person.
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Molino, A. Gelfand type problem for singular quadratic quasilinear equations. Nonlinear Differ. Equ. Appl. 23, 56 (2016). https://doi.org/10.1007/s00030-016-0409-7
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DOI: https://doi.org/10.1007/s00030-016-0409-7