Radially symmetric solutions of a class of problems of the calculus of variations without convexity assumptions (Q1196164)

The authors consider the problem of the minimisation of functionals of the form \(I(u)=\int_ B[a(| x|)u(x)+h(| x|,\Delta u(x)- \lambda u(x))]dx\), where \(\lambda\) is nonnegative, \(B\) is the unit ball and \({\partial u\over\partial n}=0\) on \(\partial B\). They show that, under certain given conditions, there is at least one radially symmetric solution for \(u\).