Reversed S-Shaped Bifurcation Curve for a Neumann Problem

Reversed S-Shaped Bifurcation Curve for a Neumann Problem

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We study the bifurcation and the exact multiplicity of solutions for a class of Square Acrylic Plaque 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.Moreover, we obtain Wallpaper that the equation has exactly either one, two, or three solutions depending on the real parameter.The stability is obtained by the eigenvalue comparison principle.