Existence of solutions for Dirichlet problems with pp-Laplacian

An existence theorem of the solutions is obtained for the pp-Laplacian equation with Dirichlet boundary conditions by using the critical point theorem developed in Song and Tang (2006) [10], Martinez and Rossi (2003) [11], where F(x,t)=∫0tf(x,s)ds is assumed to lie between the two continuous eigenvalues λk<λk+1(k≥1)λk<λk+1(k≥1) of the pp-Laplacian.