Multiplicity of solutions of a two point boundary value problem for a fourth-order equation

We study the existence of multiple solutions for semi linear fourth-order differential equation describing elastic deflections. The proof of the main result is based on a three critical point theorem.

[1]  R.E.L Turner,et al.  A class of nonlinear eigenvalue problems , 1968 .

[2]  J. Mawhin,et al.  Critical Point Theory and Hamiltonian Systems , 1989 .

[3]  Stepan Tersian,et al.  An Introduction to Minimax Theorems and Their Applications to Differential Equations , 2001 .

[4]  Alberto Cabada,et al.  Multiple solutions for discrete boundary value problems , 2009 .

[5]  D. G. Figueiredo,et al.  Lectures on the ekeland variational principle with applications and detours , 1989 .

[6]  P. Zabreiko,et al.  On the three critical points theorem. , 1998 .

[7]  J. Serrin,et al.  Extensions of the mountain pass theorem , 1984 .

[8]  Stepan Tersian,et al.  Periodic and Homoclinic Solutions of Extended Fisher–Kolmogorov Equations☆ , 2001 .

[9]  Gabriele Bonanno,et al.  Some remarks on a three critical points theorem , 2003 .

[10]  Fuyi Li,et al.  Existence and multiplicity of solutions of a kind of fourth-order boundary value problem , 2005 .

[11]  Haibo Chen,et al.  The multiplicity of solutions for fourth-order equations generated from a boundary condition , 2011, Appl. Math. Lett..

[12]  A. Iannizzotto,et al.  Multiplicity theorems for discrete boundary value problems , 2007 .

[13]  Gabriele Bonanno,et al.  A boundary value problem for fourth-order elastic beam equations , 2008 .

[14]  T. Ma.  Positive solutions for a beam equation on a nonlinear elastic foundation , 2004 .

[15]  Alberto Cabada,et al.  A note on a question of Ricceri , 2012, Appl. Math. Lett..