Convergence of regular approximations to the spectra of singular fourth-order Sturm–Liouville problems
نویسندگان
چکیده
منابع مشابه
Convergence of regular approximations to the spectra of singular fourth order Sturm-Liouville problems
We prove some new results which justify the use of interval truncation as a means of regularising a singular fourth order Sturm-Liouville problem near a singular endpoint. Of particular interest are the results in the so called lim-3 case, which has no analogue in second order singular problems.
متن کاملRegular approximations of singular Sturm-Liouville problems
Given any self-adjoint realization S of a singular Sturm-Liouville (S-L) problem, it is possible to construct a sequence {Sr} of regular S-L problems with the properties (i) every point of the spectrum of S is the limit of a sequence of eigenvalues from the spectrum of the individual members of {Sr} (ii) in the case when S is regular or limit-circle at each endpoint, a convergent sequence of ei...
متن کاملAdaptive discontinuous Galerkin approximations to fourth order parabolic problems
Abstract. An adaptive algorithm, based on residual type a posteriori indicators of errors measured in L∞(L2) and L2(L2) norms, for a numerical scheme consisting of implicit Euler method in time and discontinuous Galerkin method in space for linear parabolic fourth order problems is presented. The a posteriori analysis is performed for convex domains in two and three space dimensions for local s...
متن کاملPositive Solutions for Regular and Singular Fourth-order Boundary Value Problems∗
where 0 < β < π. By applying well-known fixed point theorems in cones, we will establish two existence results for (1.1) in the regular case and one result in the singular case. Fourth-order boundary value problems have proved to be important in applications. For example, the deformations of an elastic beam in the equilibrium state [16], whose two ends are simply supported, can be described by ...
متن کاملPositive Solutions of Singular Fourth-order Boundary-value Problems
In this paper, we present necessary and sufficient conditions for the existence of positive C3[0, 1]∩C4(0, 1) solutions for the singular boundaryvalue problem x′′′′(t) = p(t)f(x(t)), t ∈ (0, 1); x(0) = x(1) = x′(0) = x′(1) = 0, where f(x) is either superlinear or sublinear, p : (0, 1) → [0,+∞) may be singular at both ends t = 0 and t = 1. For this goal, we use fixed-point index results.
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: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
سال: 1998
ISSN: 0308-2105,1473-7124
DOI: 10.1017/s0308210500029991