An Eigenvalue Problem for a Non-bounded Quasilinear Operator

نویسندگان

  • JOSÉ CARMONA
  • ANTONIO SUÁREZ
چکیده

In this paper we study the eigenvalues associated with a positive eigenfunction of a quasilinear elliptic problem with an operator that is not necessarily bounded. For that, we use the bifurcation theory and obtain the existence of positive solutions for a range of values of the bifurcation parameter.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Eigenvalue Problems for a Quasilinear Elliptic Equation on Rn

where λ ∈ R. Next, we state the general hypotheses which will be assumed throughout the paper. (E) Assume that N , p satisfy the following relation N > p > 1. (G) g is a smooth function, at least C1,α(RN ) for some α∈ (0,1), such that g ∈ L∞(RN ) and g(x) > 0, on Ω+, with measure of Ω+, |Ω+| > 0. Also there exist R0 sufficiently large and k > 0 such that g(x) <−k, for all |x| > R0. Generally, p...

متن کامل

Existence of three solutions for a class of quasilinear elliptic systems involving the $p(x)$-Laplace operator

The aim of this paper is to obtain three weak solutions for the Dirichlet quasilinear elliptic systems on a bonded domain. Our technical approach is based on the general three critical points theorem obtained by Ricceri.

متن کامل

A Multiplicity Result for Quasilinear Problems with Nonlinear Boundary Conditions in Bounded Domains

We study the following quasilinear problem with nonlinear boundary condition −Δpu − λa x u|u|p−2 b x u|u|γ−2, in Ω and 1 − α |∇u|p−2 ∂u/∂n αu|u|p−2 0, on ∂Ω, where Ω ⊆ R is a connected bounded domain with smooth boundary ∂Ω, the outward unit normal to which is denoted by n.Δp is the p-Laplcian operator defined byΔpu div |∇u|p−2∇u , the functions a and b are sign changing continuous functions in...

متن کامل

On a nonhomogeneous quasilinear eigenvalue problem in Sobolev spaces with variable exponent

We consider the nonlinear eigenvalue problem −div ( |∇u|∇u ) = λ|u|u in Ω, u = 0 on ∂Ω, where Ω is a bounded open set in R with smooth boundary and p, q are continuous functions on Ω such that 1 < infΩ q < infΩ p < supΩ q, supΩ p < N , and q(x) < Np(x)/ (N − p(x)) for all x ∈ Ω. The main result of this paper establishes that any λ > 0 sufficiently small is an eigenvalue of the above nonhomogene...

متن کامل

Eigenvalue problems for a quasilinear elliptic equation on ℝN

where λ ∈ R. Next, we state the general hypotheses which will be assumed throughout the paper. (E) Assume that N , p satisfy the following relation N > p > 1. (G) g is a smooth function, at least C1,α(RN ) for some α∈ (0,1), such that g ∈ L∞(RN ) and g(x) > 0, on Ω+, with measure of Ω+, |Ω+| > 0. Also there exist R0 sufficiently large and k > 0 such that g(x) <−k, for all |x| > R0. Generally, p...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004