Existence and Nonexistence of Solutions for ut = div(|∇u|p − 2 ∇u) + f(∇u, u, x, t)

Existence Theorems for Inclusions of the Type (u)(t) 2 F (t; (u)(t))

For a family of operator inclusions with convex closed-valued right-hand sides in Banach spaces, the existence of solutions is obtained by chieey using Ky Fan's xed point principle. The main result of the paper improves Theorem 1 in 16] as well as Theorem 2.2 of 3]. Some meaningful concrete cases are also presented and discussed. KEY WORDS: operator inclusions in Banach spaces, Ky Fan's xed poi...

LOCAL BEHAVIOR AND GLOBAL EXISTENCE OF POSITIVE SOLUTIONS OF au − u u COMPORTEMENT LOCAL ET EXISTENCE GLOBALE DES SOLUTIONS POSITIVES DE au − u u

– We study the behavior near the origin of C2 positive solutions u(x) of au − u u (∗) in a punctured neighborhood of the origin in R (n > 2) where the constants λ and a satisfy n n−2 < λ< n+2 n−2 and 0 < a < 1. We also study the existence of C 2 positive solutions of (∗) in R. In both cases we show that changing a from one value in the open interval (0,1) to another value in (0,1) can have a dr...

Error for u = x 2

STABLE AND SINGULAR SOLUTIONS OF THE EQUATION ∆u = 1 u

We study properties of the semilinear elliptic equation ∆u = 1 u on domains in R, with an eye toward nonnegative singular solutions as limits of positive smooth solutions. We prove the nonexistence of such solutions in low dimensions when we also require them to be stable for the corresponding variational problem. The problem of finding singular solutions is related to the general study of sing...

Existence and Nonexistence of Positive Radial Solutions for Quasilinear Systems

The paper deals with the existence and nonexistence of positive radial solutions for the weakly coupled quasilinear system div (