منابع مشابه
Positive Solutions of Elliptic Equations withSingular
In this paper, a nonlinear elliptic boundary value problem with singular nonlinearity is studied, where L is a uniformly elliptic operator, is a bounded domain in R N , N 2, 0 may take the value 0 on @, and f(x; s) is possibly singular near s = 0. Some results regarding the existence of positive solutions for the problem are given under a set of hypotheses that make neither monotonicity nor str...
متن کاملPositive Solutions of Quasilinear Elliptic Equations
(1.2) { −∆pu = λa(x)|u|p−2u, u ∈ D 0 (Ω), has the least eigenvalue λ1 > 0 with a positive eigenfunction e1 and λ1 is the only eigenvalue having this property (cf. Proposition 3.1). This gives us a possibility to study the existence of an unbounded branch of positive solutions bifurcating from (λ1, 0). When Ω is bounded, the result is well-known, we refer to the survey article of Amann [2] and t...
متن کاملRadial Symmetry of Positive Solutions of Nonlinear Elliptic Equations
We study the radial symmetry and asymptotic behavior at x = 1 of positive solutions of u = '(jxj)u ; x 2 IR n and jxj large () where > 1 and '(r) is positive and continuous for r large. In particular we give conditions on ' which guarantee that each positive solution of () satisses u(x) u(jxj) ! 1 as jxj ! 1 where u(r) is the average of u on the sphere jxj = r.
متن کاملNonexistence of Positive Solutions for Some Fully Nonlinear Elliptic Equations
denote the kth elementary symmetric function, and let Γk denote the connected component of {λ ∈ R : σk(λ) > 0} containing the positive cone {λ ∈ R : λ1 > 0, · · · , λn > 0}. It is well known that Γk = {λ ∈ R : σl(λ) > 0, 1 ≤ l ≤ k}. Let S denote the set of n× n real symmetric matrices. For any A ∈ S we denote by λ(A) the eigenvalues of A. Throughout this note we will assume that Γ ⊂ R is an ope...
متن کاملPositive Solutions of Elliptic Equations with Singular Nonlinearity
In this paper, a nonlinear elliptic boundary value problem with singular nonlinearity Lu(x) = f(x, u(x)), x ∈ Ω, u(x) = φ(x), x ∈ ∂Ω, is studied, where L is a uniformly elliptic operator, Ω is a bounded domain in R , N ≥ 2, φ ≥ 0 may take the value 0 on ∂Ω, and f(x, s) is possibly singular near s = 0. Some results regarding the existence of positive solutions for the problem are given under a s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1978
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1978.75.219