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 کاملSturm-liouville Problems
Regular and singular Sturm-Liouville problems (SLP) are studied including the continuous and differentiable dependence of eigenvalues on the problem. Also initial value problems (IVP) are considered for the SL equation and for general first order systems.
متن کاملLeft-Definite Sturm-Liouville Problems
Left-definite regular self-adjoint Sturm-Liouville problems with separated and coupled boundary conditions are studied. A characterization is given in terms of right-definite problems, a concrete and “natural” indexing scheme for the eigenvalues is proposed. Pruefer transformation techniques can be used to establish the existence of and to give a characterization for the eigenvalues in the case...
متن کاملDependence of eigenvalues of Sturm-Liouville problems
The eigenvalues of Sturm-Liouville (SL) problems depend not only continuously but smoothly on boundary points. The derivative of the nth eigenvalue as a function of an endpoint satisfies a first order differential equation. This for arbitrary (separated or coupled) self-adjoint regular boundary conditions. In addition, as the length of the interval shrinks to zero all higher eigenvalues march o...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1973
ISSN: 0022-0396
DOI: 10.1016/0022-0396(73)90038-7