Nontrivial periodic solution for the superquadratic parabolic problem
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We show the existence of a nontrivial periodic solution for the superquadratic parabolic equation with Dirichlet boundary condition and periodic condition with a superquadratic nonlinear term at infinity which have continuous derivatives. We use the critical point theory on the real Hilbert space L₂(Ω x (0,2π)). We also use the variational linking theorem which is a generalization of the mountain pass theorem.
Abstract
We show the existence of a nontrivial periodic solution for the superquadratic parabolic equation with Dirichlet boundary condition and periodic condition with a superquadratic nonlinear term at infinity which have continuous derivatives. We use the critical point theory on the real Hilbert space L₂(Ω x (0,2π)). We also use the variational linking theorem which is a generalization of the mountain pass theorem.
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