Some remarks on a three critical points theorem

Abstract Some remarks on a strict minimax inequality, which plays a fundamental role in Ricceri's three critical points theorem, are presented. As a consequence, some recent applications of Ricceri's theorem to nonlinear boundary value problems are revisited by obtaining more precise conclusions.

[1]  Johnny Henderson,et al.  Multiple symmetric positive solutions for a second order boundary value problem , 2000 .

[2]  Biagio Ricceri,et al.  Existence of three solutions for a class of elliptic eigenvalue problems , 2000 .

[3]  Biagio Ricceri,et al.  Three solutions for a Neumann problem , 2002 .

[4]  P. Binding,et al.  Existence of multiple solutions of critical quasilinear elliptic Neumann problems , 2000 .

[5]  Biagio Ricceri,et al.  On a three critical points theorem , 2000 .

[6]  G. Bonanno.  A minimax inequality and its applications to ordinary differential equations , 2002 .

[7]  K. Schmitt,et al.  On the Number of Solutions of Boundary Value Problems Involving the P-Laplacian , 1996 .

[8]  S. Marano.  Elliptic eigenvalue problems with highly discontinuous nonlinearities , 1997 .

[9]  Tiancheng Ouyang,et al.  Exact multiplicity results for two classes of boundary value problems , 1993, Differential and Integral Equations.

[10]  G. Bonanno,et al.  Three solutions to a Neumann problem for elliptic equations involving the p-Laplacian , 2003 .

[11]  G. Cordaro.  On a minimax problem of ricceri , 2001 .

[12]  Dumitru Motreanu,et al.  On a three critical points theorem for non-differentiable functions and applications to nonlinear boundary value problems , 2002 .

[13]  Roberto Livrea.  Existence of three solutions for a quasilinear two point boundary value problem , 2002 .

[14]  E. Zeidler.  Nonlinear functional analysis and its applications , 1988 .

[15]  Pasquale Candito.  Existence of three solutions for a nonautonomous two point boundary value problem , 2000 .

[16]  G. Bonanno,et al.  Multiplicity theorems for the Dirichlet problem involving the p-Laplacian , 2003 .

[17]  C. O. Alves,et al.  Radially Symmetric Solutions for a Class of Critical Exponent Elliptic Problems in R N , 1996 .

[18]  G. Bonannao.  Existence of three solutions for a two point boundary value problem , 2000, Appl. Math. Lett..