In this survey we report on some recent results related to various singular phenomena arising in the study of some classes of nonlinear elliptic equations. We establish qualitative results on the existence, nonexistence or the uniqueness of solutions and we focus on the following types of problems: (i) blow-up boundary solutions of logistic equations; (ii) Lane-Emden-Fowler equations with singu...

In this paper, we will establish some new oscillation criteria for the second-order superlinear neutral delay dynamic equation of Emden-Fowler type [ a(t)(y(t) + r(t)y(τ(t))) ]∆ + p(t) |y(δ(t))| signy(δ(t)) = 0, on a time scale T; here γ > 1, a(t), r(t), τ(t), p(t) and δ(t)real-valued positive functions defined on T. Our results in the special case when T = R, improve the oscillation results fo...