We study the bifurcation and the exact multiplicity of solutions for a class of Neumann boundary value problem with indefinite weight. We prove that all the solutions obtained form a smooth reversed S-shaped curve by topological degree theory. Crandall-Rabinowitz bifurcation theorem. and the uniform antimaximum principle in terms of eigenvalues. https://allfixelectricales.shop/product-category/washing-machine-foot-pad/