State an appropriate boundary condition to ensure problem

Assignment Help Mathematics

Reference no: EM13201138

Consider the singular Sturm-Liouville eigenvalue problem

(d/dx (x du/dx))+ lambda* x^(-1) u=0
0 < x < 1;
u(1) = 0:

a) Specify an appropriate boundary condition at x = 0 to ensure that the problem is self-adjoint.

b) Use the Rayleigh quotient to show that there are no negative eigenvalues.

c) Find two linearly independent solutions to the dierential equation.

d) Find the spectrum and eigenfunctions.Consider the singular Sturm-Liouville eigenvalue problem

Reference no: EM13201138

Questions Cloud

Compute the work against gravity required to build a tower : Calculate the work against gravity required to build a tower of height 70 ft in the shape of a right circular cone with base of radius 14 ft out of brick.

Give differences in monopoly and perfectly competitive firm : Jeff Boynton,Consider the following graph:Based on the above graph, answer the following questions for a monopoly and a perfectly competitive firm. Discuss the differences you observe in above between the monopoly and perfectly competitive firm.

Explain solving rational equations : When solving rational equations, you must check your solutions to make sure you are not including extraneous solutions that are not actual solutions to the original equations.

What is the potential profit : If you can enter only one market, and the cost of entering the market is $250,000, should you enter one of the European markets. If you enter, what is your potential profit.

State an appropriate boundary condition to ensure problem : Specify an appropriate boundary condition at x = 0 to ensure that the problem is self-adjoint. b) Use the Rayleigh quotient to show that there are no negative eigenvalues.

Compute the profits-losses from the strategy : The trade is performed over one week-How do the results change under these various scenarios? Discuss your results.

What happens to the supply and demand curves : Suppose Springfield's economy moves into a recession and Y falls to $9 and rising unemployment allows widget makers to reduce wages to $18 per hour. What happens to the supply and demand curves.

State jettisoning of the solid rocket boosters : The following table gives the velocity data for a shuttle between lift off and the jettisoning of the solid rocket boosters.

Graph an equation by hand : Let C represent the total cost and x represent the number of photos produced. Graph the equation by hand. Use the graph to determine the cost of producing 7 prints.

User Account

All Pages