I know this question is a duplicate of Proof the n-th Sturm-Liouville eigenfunction has n-1 zeros. however, the link in that question's comments is broken. Also, having a proper answer to this question somewhere on the math stack exchange would be nice.
2026-03-29 02:29:14.1774751354
Why does the n-th Sturm-Liouville eigenfunction have n-1 zeros?
273 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in PARTIAL-DIFFERENTIAL-EQUATIONS
- PDE Separation of Variables Generality
- Partial Derivative vs Total Derivative: Function depending Implicitly and Explicitly on Variable
- Transition from theory of PDEs to applied analysis and industrial problems and models with PDEs
- Harmonic Functions are Analytic Evan’s Proof
- If $A$ generates the $C_0$-semigroup $\{T_t;t\ge0\}$, then $Au=f \Rightarrow u=-\int_0^\infty T_t f dt$?
- Regular surfaces with boundary and $C^1$ domains
- How might we express a second order PDE as a system of first order PDE's?
- Inhomogeneous biharmonic equation on $\mathbb{R}^d$
- PDE: Determine the region above the $x$-axis for which there is a classical solution.
- Division in differential equations when the dividing function is equal to $0$
Related Questions in EIGENFUNCTIONS
- What's wrong with the boundary condition of this $1$st order ODE?
- Find eigenfunction/eigenvalue pairs of DE
- Reference for Neumann Laplace eigenfunctions
- Does every representation of the harmonic oscillator Lie algebra necessarily admit a basis of eigenfunctions?
- Role of the interval for defining inner product and boundary conditions in Sturm Liouville problems.
- Projection onto the space spanned by eigenfunctions in a Hilbert space
- Why can we assume that these eignenfunctions are known, in the Sturm-Liouville problem?
- Is it possible to explicitly solve the inhomogeneous Helmholtz equation in a rectangle?
- Simplify the following expression by matrix calculus and orthonormal properties of eigenfunctions
- What is the equality of this integral which includes Dirac-Delta function?
Related Questions in STURM-LIOUVILLE
- Why boundary conditions in Sturm-Liouville problem are homogeneous?
- Solving Sturmian Equation
- Common solution to Integral Equation and Differential Equation
- Role of the interval for defining inner product and boundary conditions in Sturm Liouville problems.
- Orthogonality of Bessel function
- Sturm Liouville applied to a Laplace equation
- Integral transform as continuous eigenfunction expansion
- Higher order Sturm-Liouville form
- How to solve Sturm-Liouville problem $y'' + \lambda y = 0$ with unknown initial conditions?
- Is a Sturm-Liouville operator the only 2nd order linear differential operator that is self-adjoint/Hermitian?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Here is a link from the wayback machine at archive.org . Archive.org is a good place to be able to recover old links. Archive.org is maintained by the US Government. You can enter a link there to find this reference. Amazingly, this PDF was archived: https://web.archive.org/web/20220629024106/people.cs.uchicago.edu/~lebovitz/Eodesbook/sl.pdf
Thanks for the question because the PDF is a useful one. I've saved it myself. Their archive is called the Wayback Machine.