problem for Self adjoint Problems on Finite Intervals.

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So I was doing a refresher on my ODE Theory and came across this problem for Self adjoint Problems on Finite Intervals.





Let $Lx=-(px')'+qx, $ where $p$ is of Class $C^1$and $q$ of class $C$ on $[a,b]$ and $p ne 0$ on [a,b]. Let $Ux=0$ be given by $$alpha x(a)+ beta x'(a)=0 $$ $$gamma x(b)+ delta x' (b)=0$$.



Show the problem $pi$ is self adjoint if and only if $p$ and $q$ are real, $$gamma bardelta=bargammadelta $$$$ alpha barbeta=baralpha beta$$ Which is requiring that $alpha , beta , gamma, delta $ all be real.





Any help on this problem will be greatly appreciated in Advance.




differential-equations




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    So I was doing a refresher on my ODE Theory and came across this problem for Self adjoint Problems on Finite Intervals.





    Let $Lx=-(px')'+qx, $ where $p$ is of Class $C^1$and $q$ of class $C$ on $[a,b]$ and $p ne 0$ on [a,b]. Let $Ux=0$ be given by $$alpha x(a)+ beta x'(a)=0 $$ $$gamma x(b)+ delta x' (b)=0$$.



    Show the problem $pi$ is self adjoint if and only if $p$ and $q$ are real, $$gamma bardelta=bargammadelta $$$$ alpha barbeta=baralpha beta$$ Which is requiring that $alpha , beta , gamma, delta $ all be real.





    Any help on this problem will be greatly appreciated in Advance.




    differential-equations




    share|cite|improve this question





















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      So I was doing a refresher on my ODE Theory and came across this problem for Self adjoint Problems on Finite Intervals.





      Let $Lx=-(px')'+qx, $ where $p$ is of Class $C^1$and $q$ of class $C$ on $[a,b]$ and $p ne 0$ on [a,b]. Let $Ux=0$ be given by $$alpha x(a)+ beta x'(a)=0 $$ $$gamma x(b)+ delta x' (b)=0$$.



      Show the problem $pi$ is self adjoint if and only if $p$ and $q$ are real, $$gamma bardelta=bargammadelta $$$$ alpha barbeta=baralpha beta$$ Which is requiring that $alpha , beta , gamma, delta $ all be real.





      Any help on this problem will be greatly appreciated in Advance.




      differential-equations




      share|cite|improve this question











      So I was doing a refresher on my ODE Theory and came across this problem for Self adjoint Problems on Finite Intervals.





      Let $Lx=-(px')'+qx, $ where $p$ is of Class $C^1$and $q$ of class $C$ on $[a,b]$ and $p ne 0$ on [a,b]. Let $Ux=0$ be given by $$alpha x(a)+ beta x'(a)=0 $$ $$gamma x(b)+ delta x' (b)=0$$.



      Show the problem $pi$ is self adjoint if and only if $p$ and $q$ are real, $$gamma bardelta=bargammadelta $$$$ alpha barbeta=baralpha beta$$ Which is requiring that $alpha , beta , gamma, delta $ all be real.





      Any help on this problem will be greatly appreciated in Advance.





      differential-equations





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      share|cite|improve this question




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