In this paper, we discuss the existence, nonexistence, and multiplicity of positive solutions for a class of singular eigenvalue problems. Some of our theorems are new, while others extend earlier results obtained by Zhang and Kong [12]. The interesting point is that the authors obtain the relation between the existence of solutions and the parameter λ. The arguments are based on the fixed poin...

We study the global existence and the global nonexistence of a non-Newtonian polytropic filtration system coupled via nonlinear boundary flux. We first establish a weak comparison principle, then discuss the large time behavior of solutions by using modified upper and lower solution methods and constructing various upper and lower solutions. Necessary and sufficient conditions on the global exi...

We study the existence and nonexistence of positive singular solutions to second–order non-divergence type elliptic inequalities in the form N ∑ i,j=1 aij(x) ∂u ∂xi∂xj + N ∑ i=1 bi(x) ∂u ∂xi ≥ K(x)u, −∞ < p <∞, with measurable coefficients in a punctured ball BR \{0} of R , N ≥ 1. We prove the existence of a critical value p∗ that separates the existence region from non-existence. In the critic...