Periodic solutions of p-Laplacian systems with a nonlinear convection term (original) (raw)

Existence of infinitely many periodic solutions for ordinary p-Laplacian systems

Journal of Mathematical Analysis and Applications, 2009

In this paper, we study the existence and multiplicity of non-trivial periodic solutions of ordinary p-Laplacian systems by using the minimax technique in critical point theory. We also give an example to illustrate that the obtained results are new even in the case p = 2.

Periodic Solutions of Singular Nonlinear Perturbations of the Ordinary p-Laplacian

Advanced Nonlinear Studies, 2002

Using some recent extensions of upper and lower solutions techniques and continuation theorems to the periodic solutions of quasilinear equations of p-Laplacian type, we prove the existence of positive periodic solutions of equations of the form (|xʹ|p-2xʹ)ʹ + f(x)xʹ + g(x) = h(t) with p > 1, f arbitrary and g singular at 0. This extends results of Lazer and Solimini for the undamped ordinary differential case.

New results on the existence of periodic solutions to a p-Laplacian differential equation with a deviating argument

Journal of Mathematical Analysis and Applications, 2007

By means of Mawhin's continuation theorem, a kind of p-Laplacian differential equation with a deviating argument as follows: ϕ p x (t) = f t, x(t), x t − τ (t) , x (t) + e(t) is studied. Some new results on the existence of periodic solutions are obtained. The main results (Theorems 3.2 and 3.3) are all related to the deviating argument τ (t). Meanwhile, the degrees with respect to the variables x 0 , x 1 of f (t, x 0 , x 1 , x 2) are allowed to be grater than p − 1, which is different from the corresponding conditions of known literature.

Periodic mathrmLp\mathrm{L}_{p}mathrmLp Estimates by ℛ-Boundedness: Applications to the Navier-Stokes Equations

Acta Applicandae Mathematicae

General evolution equations in Banach spaces are investigated. Based on an operator-valued version of de Leeuw’s transference principle, time-periodic mathrmLp\mathrm {L}_{p}mathrmLp L p estimates of maximal regularity type are carried over from ℛ-bounds of the family of solution operators (ℛ-solvers) to the corresponding resolvent problems. With this method, existence of time-periodic solutions to the Navier-Stokes equations is shown for two configurations: in a periodically moving bounded domain and in an exterior domain, subject to prescribed time-periodic forcing and boundary data.

Multiple nontrivial solutions for nonlinear periodic problems with the p-Laplacian

Journal of Differential Equations, 2007

We consider a nonlinear periodic problem driven by the scalar p-Laplacian with a nonsmooth potential (hemivariational inequality). Using the degree theory for multivalued perturbations of (S) + -operators and the spectrum of a class of weighted eigenvalue problems for the scalar p-Laplacian, we prove the existence of at least three distinct nontrivial solutions, two of which have constant sign.

Periodic solutions for second order differential inclusions with the scalar p-Laplacian

Journal of Mathematical Analysis and Applications, 2006

We study periodic problems driven by the scalar p-Laplacian with a multivalued right-hand side nonlinearity. We prove two existence theorems. In the first, we assume nonuniform nonresonance conditions between two successive eigenvalues of the negative p-Laplacian with periodic boundary conditions. In the second, we employ certain Landesman-Lazer type conditions. Our approach is based on degree theory.