Question: EXERCISE 1.40. (i) Show there is exactly one u C([1,1]) that satisfies the integral equation X u(x) = x [* 1 cos(u(1)) dt, x

EXERCISE 1.40. (i) Show there is exactly one u C([1,1]) that satisfies

EXERCISE 1.40. (i) Show there is exactly one u C([1,1]) that satisfies the integral equation X u(x) = x ["* 1 cos(u(1)) dt, x [1, 1]. Hint: Use the contraction principle in the space C([-1,1]). (ii) Show that u is differentiable. Is u' differentiable?

Step by Step Solution

★★★★★

3.50 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

X 2 we using seperation T Let Have to solve U2 1 dx Cuxx Utt d72 dx2 ux 12 ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...

The joint probability distribution of the number X of cars and the number Y of buses per signal cycle at a proposed left-turn lane is displayed in the accompanying joint probability table. a. What is...

Prolog is a language that is suitable for solving problems in the field of artificial intelligence. That is, it can be used to solve problems that used to be solvable only by human brains. In this...

[32] Show that there exists an immune set I (a set without an infinite computably enumerable subset, for instance the complement of a set B as in Theorem 2.7.1, Item (iii)), such that there is a...

The homogeneous diffusion equation (5.160) for the vector potential for quasi-static fields in unbounded conducting media has a solution to the initial value problem ?of the form, A(x, t) = ? d 3 x'...

(a) Show that the lVP y' = j(t, y), y( to) = yo is equivalent to the integral equation by verifying the following two statements: (i) Every solution y( t) of the IVP satisfies the integral equation;...

Exercise 9.7 In the RMV recovery formulation, show that the price C(t) given by (9.19) satisfies the integral equation (9.18). Hint: Use the Cox process argument. Note that, for s > t, s-1 Qt{T =...

In Section 9.3 we looked at mixing problems in which the volume of fluid remained constant and saw that such problems give rise to separable equations. (See Example 6 in that section.) If the rates...

When a one-parameter family of curves satisfies a first-order DE, we can find another such family as solution curves of a related DE with the property that a curve of the other family orthogonally....

10.4. Hydrodynamics of an ideal fluid in two dimensions Consider the stationary motion of an incompressible and irrotational fluid in two dimensions. Denoting by v(x, y) = (v1, v2) the vector field...

need help asap XAUSPDUSDNRUSDSEK=46.0485/35=5.8525/35 Calculate cross rate between 100 INR/SEKquotations VSD

Question 1: A company manufacturing a product exclusively for the customers in its home country should not invest in global operations to source raw materials and components for its product....

Fletcher Fabrication, Inc., produces three products by a joint production process. Raw materials are put into production in Department X, and at the end of processing in this department, three...

Brenda apologized to Kordell for an e - mail that upset him. She said she had chosen an inconsiderate way of stating her idea, and that she d be happy to discuss it further. Brenda is Multiple...

Serverless technologies is a good practice for Question 41 options: Security Excellence Operational Excellence Performance Excellence Cost Optimization Excellence

ttached File(s): Psych Discussion Rubric Moral Theory Read pages 300-309 of your text. There are two general types of moral theories: (1) Morality is relative and (2) Morality is universal. Which of...

1. The income statement of Bjorn ASA for the month of July shows net income of 2,841 based on Service Revenue 6,939, Salaries and Wages Expense 2,317, Supplies Expense 1,219, and Utilities Expense...

Nike manufactures shoes and sportswear. How has the Internet changed the way this company communicates with its suppliers and retail customers?

Consider a random sample of size n from a continuous distribution having median 0 so that the probability of any one observation being positive is .5. Disregarding the signs of the observations, rank...

Hexavalent chromium has been identified as an inhalation carcinogen and an air toxin of concern in a number of different locales. The article "Airborne Hexavalent Chromium in Southwestern Ontario"...

The article "Exhaust Emissions from Four-Stroke Lawn Mower Engines" (J. of the Air and Water Mgmnt. Assoc., 1997: 945-952) reported data from a study in which both a baseline gasoline mixture and a...

The histogram displays the sugar content (as a percent of weight) of 49 brands of breakfast cereals. a) Describe this distribution. b) What do you think might account for this shape?

The table given below shows the number of licensed U.S. drivers (in millions) by age and by sex (www.dot.gov). a) What percent of total drivers are under 20? b) What percent of total drivers are...

The Centers for Disease Control and Prevention (CDC) has estimated that 19.8% of Americans over 15 years old are obese. The CDC conducts a survey on obesity and various behaviors. Here is a table on...