and for λ λ ≥ ≥ 0 , a real solution exists only for λ λ ∈ ∈ [ 0 , λ λ c ] , where λ λ c is the critical parameter called as Frank-Kamenetskii parameter. The critical parameter is λ λ c = 0.8785 for n = 1 , λ λ c = 2 for n = 2 and λ λ c = 3.32 for n = 3 . For n = 1 , 2 , two solution exists and for 3 ≤ ≤ n ≤ ≤ 9 infinitely many solution exists with solutions oscillating about the point λ λ = 2 ( n − − 2 ) . For n ≥ ≥ 10 , the solution is unique and in these cases the critical parameter is given by λ λ c = 2 ( n − − 2 ) . Multiplicity of solution for n = 3 was discovered by Israel Gelfand in 1963 and in later 1973 generalized for all n by Daniel D. Joseph and Thomas S. Lundgren.