Radial Solutions of Quasilinear Elliptic Differential Equations

On a Class of Singular Sublinear p-Laplacian Problems

“…Problem (1.1) occurs in the study of radial solutions for the p-Laplacian boundary value problem Àdivðj'uj pÀ2 'uÞ ¼ lf ðuÞ in W u ¼ 0 on qW; ð1:2Þ where W is the annulus 0 < a < jxj < b, x A R N . For the literature on this problem when f is nonsingular, we refer to [3] and the references therein. In [1,7], existence results for positive solutions of (1.1) with f allowed to be singular at 0 and sign-changing were obtained for p ¼ 2, r 1 1 and f superlinear at y.…”

Bounded solutions of a k -Hessian equation involving a weighted nonlinear source

“…We point out that (2k + σ) − a σ = 0 is equivalent to defining q = q * (k, σ). We first note that (2k + σ) − a σ < 0 is equivalent to q > q * (k, σ) and by Lemma 3.1 there exists a unique classical global solution of (31). In case (2k + σ) − a σ > 0 (i.e.…”

“…Next we show that the orbits of system (14) start from (n + σ, 0) and end at (x,ŷ). By (12) and (31), the function y = y(t) satisfies…”

Existence of positive radial solutions for superlinear, semipositone problems on the exterior of a ball

“…Here, the reaction term f : [0, ∞) → R is a nondecreasing, C 1 function such that The case when f (0) < 0 is referred to in the literature as a semipositone problem, and it has been well documented (see [22], [6]) that they pose considerably more challenges in the study of positive solutions than the case where f (0) > 0 (positone problems). For a rich history of superlinear, semipositone problems on bounded domains with Dirichlet boundary conditions, see [2], [3], [4], [5], [7], [8], [10], [11], [12], [13], [14], [15], [16], [20], [21], and [26]. The main focus of this paper is to extend an important existence result for λ ≈ 0 obtained in the case of bounded domains with Dirichlet boundary conditions to a domain exterior to a ball, and also to problems involving classes of nonlinear boundary conditions on the boundary of the ball.…”