Estimation on the first eigenvalue for some nonlinear Dirichlet eigenvalue problems Original Research Article

In this paper we show the existence of local analytic solution for the nonlinear eigenvalue problem View the MathML source(rN−1Φp(v′))′+λrN−1Φq(v)=0(p,q>0,N≥1),r>0 with View the MathML sourceΦm(s)=|s|m−1s,s∈R,m>0 and v(0)=1,v′(0)=0v(0)=1,v′(0)=0. By applying the J.C.P. Miller formula we get recursion formulas for the determination of the coefficients. Using the coefficients of the power series form we give estimates for the smallest eigenvalue λ1λ1 by Graeffe’s method.