Bifurcation of nonlinear elliptic system from the first eigenvalue
نویسندگان
چکیده
منابع مشابه
Spectral asymptotics and bifurcation for nonlinear multiparameter elliptic eigenvalue problems
This paper is concerned with the nonlinear multiparameter elliptic eigenvalue problem u′′(r) + N − 1 r u′(r) + μu(r)− k ∑ i=1 λifi(u(r)) = 0, 0 < r < 1, u(r) > 0, 0 ≤ r < 1, u′(0) = 0, u(1) = 0, where N ≥ 1, k ∈ N and μ, λi ≥ 0 (1 ≤ i ≤ k) are parameters. The aim of this paper is to study the asymptotic properties of eigencurve μ(λ, α) = μ(λ1, λ2, · · · , λk, α) with emphasis on the phenomenon ...
متن کاملSimplicity and stability of the first eigenvalue of a nonlinear elliptic system
Note that the system (1.1) is of two second-order elliptic equations. It is weakly coupled in the sense that interaction is present only in the “source terms,” while the differential terms have only one dependent variable. The differential operator involved is the so-called p-Laplacian, that is, ∆pu = ∇ · (|∇u|p−2∇u), which reduces to the ordinary Laplace operator ∆u when p = 2. We mention that...
متن کاملGlobal bifurcation and continua of nonnegative solutions for some nonlinear elliptic eigenvalue type problems
In this note, we study the existence and multiplicity of solutions, strictly positive or nonnegative having a dead core (where the solution vanishes) of several nonlinear problems of eigenvalue type. 2000 Mathematics Subject Classification: 35J60, 35B52.
متن کاملVariational Methods for Nonlinear Elliptic Eigenvalue Problems
In the present note, we give a simple general proof for the existence of solutions of the following two types of variational problems: PROBLEM A. To minimize fa F(x> u, • • • , Du)dx over a subspace VofW>*(tt). PROBLEM B. TO minimize ƒ« F(x, w, • • • , Du)dx for u in V with / a G(x, u, • • • , D^u)dx^c. The solution of the first problem yields a weak solution of a corresponding elliptic boundar...
متن کاملOrlicz Spaces and Nonlinear Elliptic Eigenvalue Problems
Nonlinear elliptic differential equations of order m acting in a space of m dimensions often occupy a special position in more general theories. In this paper we shall study one aspect of this situation. The nonlinear problem under consideration will be the variational approach to eigenvalue problems for nonlinear elliptic partial differential equations as developed by the author in [l], [2], [...
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: Electronic Journal of Qualitative Theory of Differential Equations
سال: 2003
ISSN: 1417-3875
DOI: 10.14232/ejqtde.2003.1.21