Please answer Q4

4. Let L be the same operator as in the problem 3(a). Find the sufcient condition for q(a:), a(m),[3 (:13) such that all eigenvalues for the problem L[u] = A0(a:)u subject to the same boundary condition in the problem (3) are positive, Where 0(m) > 0 on Q. 3. Let 2 be a bounded domain in R" with boundary On and n > 1. Let a(x) > 0 on n and b(x) be continuous on 2. Consider L[u] : = Vla(x) Vul + q(2) u, x En, Blu] = a(2)a(x) Vnu + B(x)u = 0, x E an, where a(x) and (x) are continuous and a(x)2 + 3(x)2 > 0 on an. (a) Prove that the operator L is self-adjoint