Existence of infinitely many nodal solutions for a superlinear Neumann boundary value problem

Existence of Infinitely Many Nodal Solutions for a Superlinear Neumann Boundary Value Problem

INFINITELY MANY SOLUTIONS FOR A CLASS OF P-BIHARMONIC PROBLEMS WITH NEUMANN BOUNDARY CONDITIONS

The existence of infinitely many solutions is established for a class of nonlinear functionals involving the p-biharmonic operator with nonhomoge- neous Neumann boundary conditions. Using a recent critical-point theorem for nonsmooth functionals and under appropriate behavior of the nonlinear term and nonhomogeneous Neumann boundary conditions, we obtain the result.

Infinitely Many Solutions for a Robin Boundary Value Problem

Aixia Qian1 and Chong Li2 1 School of Mathematic Sciences, Qufu Normal University, Qufu Shandong 273165, China 2 Institute of Mathematics, AMSS, Academia Sinica, Beijing 100080, China Correspondence should be addressed to Aixia Qian, [email protected] and Chong Li, [email protected] Received 29 August 2009; Accepted 7 November 2009 Academic Editor: Wenming Zou Copyright q 2010 A. Qian and C. L...

infinitely many solutions for a class of p-biharmonic problems with neumann boundary conditions

the existence of infinitely many solutions is established for a class of nonlinear functionals involving the p-biharmonic operator with nonhomoge- neous neumann boundary conditions. using a recent critical-point theorem for nonsmooth functionals and under appropriate behavior of the nonlinear term and nonhomogeneous neumann boundary conditions, we obtain the result.

Infinitely many singularities and denumerably many positive solutions for a second-order impulsive Neumann boundary value problem

where M is a positive constant, J = [, ], tk ∈ R, k = , . . . ,m, m ∈ N, satisfy  = t < t < t < · · · < tm < tm+ = , – x|t=tk denotes the jump of x′(t) at t = tk , that is, – x|t=tk = x′((tk)+) – x′((tk)–), here x′((tk)+) and x′((tk)–), respectively, represent the right-hand limit and left-hand limit of x′(t) at t = tk . In addition, ω, f and Ik satisfy the following conditions: (H) ω...