In the present paper we study the Dirichlet boundary value problem for quasilinear elliptic equations including non-uniformly and degenerate ones. In particular, we consider mean curvature equation and pseudo p-Laplace equation as well. It is well-known that the proof of the existence of continuous viscosity solutions is based on Ishii’s implementation of Perron’s method. In order to use this m...

and Applied Analysis 3 we refer to 20–22 , but the results on the boundary blow-up solutions for p x -Laplacian equations are rare see 16 . In 16 , the present author discussed the existence and asymptotic behavior of boundary blow-up solutions for the following p x -Laplacian equations: −Δp x u f x, u 0, in Ω, u x −→ ∞, as d x, ∂Ω −→ 0, 1.8 on the condition that f x, · satisfies polynomial gro...

Where changes to a solution introduce additional expenses or reorganization, solution robustness is a valuable property. A robust solution is less sensitive to changes. For example, a robust schedule will not collapse immediately when one job takes slightly longer to execute than planned. The schedule should change locally and in small proportions, and the overall makespan should change little ...

and Applied Analysis 3 1, 2, 6–9 and the references cited therein . For blowup results for other parabolic systems, we refer the readers to 10–13 and the references cited therein. Moreover, in recent years, many authors see studies such as those in 14, 15 and the references cited therein considered semilinear reaction-diffusion systems with nonlocal Dirichlet boundary conditions of the form ut ...

and Applied Analysis 3 x 1. That is, sin πx > 0 in 0, 1 but, for η large enough, the corresponding solution is not positive. This contrasts with the local equation −u′′ x ηu x f x , 0 < x < 1, u 0 u 1 0, η > 0, 1.8 for which it is very well known, see 14 , that, for all η > 0, function u > 0 in 0, 1 whenever f > 0 in 0, 1 . Remark 1.1. We have to point out that the lack of a general maximum pri...