Nonlinear Perturbations of a Periodic Quasilinear Elliptic Problem with Discontinuous Nonlinearity in RN1
Qin Li
Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Jiangsu Nanjing 210023, China.
Zuodong Yang *
Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Jiangsu Nanjing 210023, China.
*Author to whom correspondence should be addressed.
Abstract
Using variational methods, we estabilish existence of positive solutions for a class of quasilinear
elliptic problems
where 
is a positive, continuous perturbations of a
periodic function, H is the Heaviside function and f is a continuous function with subcritical growth.
The results of the semilinear equations are extended to the quasilinear problem.
Keywords: Nonlinear perturbations, discontinuous nonlinearity, quasilinear elliptic problem, periodic.