Singular curve and critical curve for doubly nonlinear Lane–Emden type equations

Abstract

This paper is concerned with singular curve and critical curve for the periodic doubly nonlinear Lane–Emden type equation . In 2010, under a convex assumption on the domain Ω, Wang et al. (2010) considered a partial case of . While, there are no results about the cases of and before the present work. In this paper, we fill the gap for these two cases and give a total classification for the exponents. Furthermore, by constructing a special blow‐up sequence, we remove the convex assumption on the domain Ω, not only for the partial case considered in Wang et al. (2010) but also for other remaining cases.