Periodic solutions of a class of quasilinear parabolic equations
Guanghui Fan · Journal of Natural Science of Heilongjiang University · 2012
The Dirichlet boundary value problem of a class of quasilinear parabolic equations with periodic reaction term is considered.Since the equation is nonlinear and degenerate,the existence of the weak solutions of the problem is only involved.The key is how to construct a pair of ordered supersolution and subsolution.By using the first eigenvalue and the corresponding eigenfunction of the p-Laplacian,a pair of ordered T-periodic supersolution and subsolution is constructed.Then by using the monotonicity method,the existence of nontrivial nonnegative periodic solutions is obtained.