Infinitely Many Solutions for a Boundary Value Problem with Discontinuous Nonlinearities

Infinitely Many Solutions for a Boundary Value Problem with Discontinuous Nonlinearities

The existence of infinitely many solutions for a Sturm-Liouville boundary value problem, under an appropriate oscillating behavior of the possibly discontinuous nonlinear term, is obtained. Several special cases and consequences are pointed out and some examples are presented. The technical approach is mainly based on a result of infinitely many critical points for locally Lipschitz functions.

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 Radial Solutions for a Sub-Super Critical Dirichlet Boundary Value Problem in a Ball

We prove the existence of infinitely many solutions to a semilinear Dirichlet boundary value problem in a ball for a nonlinearity g(u) that grows subcritically for u positive and supercritically for u negative.

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