Global bifurcation and continua of nonnegative solutions for some nonlinear elliptic eigenvalue type problems
نویسندگان
چکیده
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.
منابع مشابه
Existence, Multiplicity, and Bifurcation in Systems of Ordinary Differential Equations
We prove new non-resonance conditions for boundary value problems for two dimensional systems of ordinary differential equations. We apply these results to the existence of solutions to nonlinear problems. We then study global bifurcation for such systems of ordinary differential equations Rotation numbers are associated with solutions and are shown to be invariant along bifurcating continua. T...
متن کاملBranches of positive and free boundary solutions for some singular quasilinear elliptic problems
We study the existence and multiplicity of solutions, strictly positive or nonnegative having a free boundary (the boundary of the set where the solution vanishes) of some one-dimensional quasilinear problems of eigenvalue type with possibly singular nonlinear terms. © 2008 Elsevier Inc. All rights reserved.
متن کاملEigenvalue Problems for Degenerate Nonlinear Elliptic Equations in Anisotropic Media
We study nonlinear eigenvalue problems of the type −div(a(x)∇u) = g(λ,x,u) in RN , where a(x) is a degenerate nonnegative weight. We establish the existence of solutions and we obtain information on qualitative properties as multiplicity and location of solutions. Our approach is based on the critical point theory in Sobolev weighted spaces combined with a Caffarelli-Kohn-Nirenberg-type inequal...
متن کاملNonlinear elliptic boundary value problems versus their finite difference approximations : numerically irrelevant solutions
The aim of this paper is to continue and extend the discussion in [9] concerning the 'numerically irrelevant' Solutions NIS' of finite difference approximations to certain nonlinear boundary value problems in the context of continuation methods or more generally and more appropriately, in the context of global topological perturbations of nonlinear eigen value problems. This latter technique äs...
متن کاملGlobal bifurcation and nodal solutions for fourth-order problems with sign-changing weight
In this paper, we shall establish unilateral global bifurcation result for a class of fourthorder eigenvalue problems with sign-changing weight. Under some natural hypotheses on perturbation function, we show that lk;0 is a bifurcation point of the above problems and there are two distinct unbounded continua, Ck þ and Ck , consisting of the bifurcation branch Ck from lk;0 , wher e lk is the kth...
متن کاملذخیره 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