= Problem (F'02, #2). Consider the second order differential operator L defined by Lu=-u" + eru for 0 < r < 7 with bound

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Problem F 02 2 Consider The Second Order Differential Operator L Defined By Lu U Eru For 0 R 7 With Bound 1 (31.34 KiB) Viewed 58 times

= Problem (F'02, #2). Consider the second order differential operator L defined by Lu=-u" + eru for 0 < r < 7 with boundary conditions u(0) = u(t)=0. a) For € = 0 find the leading (i.e. smallest) eigenvalue to and the corresponding eigenfunction oo for L. b) For e > 0 look for the eigenvalues and eigenfunctions to have an erpansion of the form 1 = 10 + eli + O(), 0 00+ €oi + 0(?). Find formulas for li and 01 (your formulas will contain definite integrals which you do not need to evaluate).