Infinitely Many Solutions For P-Laplacian Inclusion Systems

Variational inclusion system is an important branch of nonlinear analytic theory.It covers more aspects than general variational equations, such as linear time invariantsystem, interval system, and polychoron system. It arises from the progress of cybernet-ics and the research of noncontinuous variational equations. It has been wisely used todescribe dynamic systems of Economics, Sociology and bioscience as well as adaptivecontrol system.In this paper, we consider the p-Laplacian variational inclusion systems of the form:where2≤N <p <+∞and α(x)∈L~1(RN)∩L∞(R~N) is radially symmetric. F: R~2â†'Ris a locally lipschitz but not necessary smooth potential function andâ–³pu=div(|u|~p-~2(?) u).While (?)1F(u, v) is the partial generalized gradient of F(·, v) at u and (?)2F(u, v) is that ofF(u,·) at v. Under some suitable growth conditions but without symmetry assumptions onF, we show the existence of infinitely many radially symmetric solutions of the systems(P). Our approach is based on a non-smooth Ricceri-type variation principle, developedby Marano and Motreanu[14](J. Dif. Eqns.2002(182):108-120).