Results 1 to 4 of 4
Like Tree1Thanks
  • 1 Post By chiro

Math Help - Integral equations

  1. #1
    Member
    Joined
    Jul 2009
    Posts
    111
    Thanks
    1

    Lightbulb Integral equations

    When does the integral equation given by

     y(x) = 1 + \lambda \int_{0}^{\frac{\pi} {2}} {cos (x-t) y(t) dt have

    i) a unique solution ???
    ii) no solution???

    Some head start with this question will be of great help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,612
    Thanks
    591

    Re: Integral equations

    Hey MAX09.

    Have you tried differentiating the integral in order to get a differential equation to solve?

    Differentiation under the integral sign - Wikipedia, the free encyclopedia

    Also Lipschitz continuity is a good way to show existence of differential equations.

    Lipschitz continuity - Wikipedia, the free encyclopedia
    Thanks from MAX09
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jul 2009
    Posts
    111
    Thanks
    1

    Re: Integral equations

    Chiro, Thanks for your suggestion. I tried along those lines, but it seems I need specific literature on Linear Integral Equations.
    A hint or a link in that direction will definitely give me a headstart.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Aug 2011
    Posts
    243
    Thanks
    56

    Re: Integral equations

    in the integral cos(x-t) = cos(x)cos(t)+sin(x)sin(t)
    Leading to y = 1+lambda *(A*cos(x)+B*sin(x))
    where A and B are constant (definite integrals where there is no x into them)
    Bringing back y = 1+lambda *(A*cos(x)+B*sin(x)) into the equation, after integration we obtain two relationships so that the coefficient of sin(x) and cos(x) are = 0.
    This leads to : A = B = -4 / (pi+2-(4/lambda))
    Conclusion : There is one solution.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Need help with integral of three equations
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: April 7th 2012, 06:21 AM
  2. Integral equations #3
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: September 15th 2010, 10:58 AM
  3. Integral equations
    Posted in the Advanced Applied Math Forum
    Replies: 5
    Last Post: July 21st 2010, 09:06 AM
  4. Integral equations
    Posted in the Calculus Forum
    Replies: 2
    Last Post: July 25th 2009, 04:45 AM
  5. Question concerning integral equations
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 10th 2008, 04:43 AM

Search Tags


/mathhelpforum @mathhelpforum