منابع مشابه
Second Order Sturm-liouville Problems with Asymmetric, Superlinear Nonlinearities
We consider the nonlinear Sturm-Liouville problem −(p(x)u′(x))′ + q(x)u(x) = f(x, u(x), u′(x)), in (0, π), (1) c00u(0) + c01u ′(0) = 0, c10u(π) + c11u ′(π) = 0, (2) where p ∈ C1[0, π], q ∈ C0[0, π], with p(x) > 0, x ∈ [0, π], and ci0 + ci1 > 0, i = 0, 1. We suppose that f : [0, π] × R2 → R is continuous and there exist increasing functions ζl, ζu : [0,∞) → R, and a constant B, such that limt→∞ ...
متن کاملSecond Order, Sturm-liouville Problems with Asymmetric, Superlinear Nonlinearities Ii
We consider the nonlinear Sturm-Liouville problem −(p(x)u′(x))′ + q(x)u(x) = f(x, u(x)) + h(x), in (0, π), c00u(0) + c01u ′(0) = 0, c10u(π) + c11u ′(π) = 0, where: p ∈ C1[0, π], q ∈ C0[0, π], with p(x) > 0 for all x ∈ [0, π]; ci0 + ci1 > 0, i = 0, 1; h ∈ L2(0, π). We suppose that f : [0, π] × R → R is continuous and there exist increasing functions ζl, ζu : [0,∞)→ R, and positive constants A, B...
متن کاملExtremal Eigenvalues for a Sturm-Liouville Problem
We consider the fourth order boundary value problem (ry′′)′′+(py′)′+ qy = λwy, y(a) = y′(a) = y(b) = y′(b) = 0, which is used in a variety of physical models. For such models, the extremal values of the smallest eigenvalue help answer certain optimization problems, such as maximizing the fundamental frequency of a vibrating elastic system or finding the tallest column that will not buckle under...
متن کاملInverse Sturm-Liouville problem with discontinuity conditions
This paper deals with the boundary value problem involving the differential equation begin{equation*} ell y:=-y''+qy=lambda y, end{equation*} subject to the standard boundary conditions along with the following discontinuity conditions at a point $ain (0,pi)$ begin{equation*} y(a+0)=a_1 y(a-0),quad y'(a+0)=a_1^{-1}y'(a-0)+a_2 y(a-0), end{equation*} where $q(x), a_1 , a_2$ are rea...
متن کاملinverse sturm-liouville problem with discontinuity conditions
this paper deals with the boundary value problem involving the differential equationbegin{equation*} ell y:=-y''+qy=lambda y, end{equation*} subject to the standard boundary conditions along with the following discontinuity conditions at a point $ain (0,pi)$ begin{equation*} y(a+0)=a_1 y(a-0),quad y'(a+0)=a_1^{-1}y'(a-0)+a_2 y(a-0),end{equation*}where $q(x), a_1 , a_2$ are real, $qin l...
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: Transactions of the American Mathematical Society
سال: 1962
ISSN: 0002-9947
DOI: 10.2307/1993658