We consider weak positive solutions of the equation −∆mu = f(u) in the halfplane with zero Dirichlet boundary conditions. Assuming that the nonlinearity f is locally Lipschitz continuous and f(s) > 0 for s > 0, we prove that any solution is monotone. Some Liouville type theorems follow in the case of Lane-Emden-Fowler type equations. Assuming also that |∇u| is globally bounded, our result impli...

We show the existence of (H2 0 (Ω)×L2(Ω), H2 0 (Ω)×H2 0 (Ω))-global attractors for plate equations with critical nonlinearity when g ∈ H−2(Ω). Furthermore we prove that for each fixed T > 0, there is an (H2 0 (Ω) × L2(Ω), H2 0 (Ω) × H2 0 (Ω))T -exponential attractor for all g ∈ L2(Ω), which attracts any H2 0 (Ω)×L2(Ω)-bounded set under the stronger H2(Ω)×H2(Ω)-norm for all t ≥ T .

We introduce a novel concept of surface bound states in the continuum, i.e., surface modes embedded into the linear spectral band of a discrete lattice. We suggest an efficient method for creating such surface modes and the local bounded potential necessary to support the embedded modes. We demonstrate that the surface embedded modes are structurally stable, and the position of their eigenvalue...

Based on Lyapunov stability theorem, a method is proposed for feedback synchronization with parameters perturbation and external disturbances. It is proved theoretically that if the perturbation and disturbances are bounded, the synchronization error can be ensured to approach to and stay within the pre-specified bound which can be arbitrarily small. Some typical chaotic systems with different ...

In this short article, we study the blow-up properties of solutions to a parabolic problem with a gradient nonlinearity under homogeneous Dirichlet boundary conditions. By constructing an auxiliary function and by modifying the first order differential inequality technique introduced by Payne et al., we obtain a lower bound for the blow-up time of solutions in a bounded domain Ω ⊂ Rn for any n ...

The upper and lower bounds for asymptotic stability (AS) of a time-variant discrete-time nonlinear system with bounded parameter perturbations are provided. The analysis is undertaken for a class of nonlinear relaxation systems with the saturation nonlinearity of sigmoid type. Based upon the theory of convex polytopes and underlying linear relaxation equation, the bounds of the stability region...

An Integral Sliding Mode (ISM) based robustified Linear Parameter Varying (LPV) control is presented for a laboratory scale ball on beam balancer system. The inherent input channel nonlinearity and under-actuated coupled dynamics make it challenging problem. ISM control, being famous reaching phase elimination, operates under the action of which usually an algebraic sum continuous discontinuous...

Networked Control Systems (NCSs) has been recognized as an area where theory is behind the development of technology. The defining feature of NCSs can be considered as the information is exchanged through a network among control system components. So the network induced time delay is inevitable in NCSs. The time delay may degrade the performance of control systems and even destabilize the syste...

We carry out an investigation of the existence infinitely many solutions to a fractional p-Kirchhoff-type problem with singularity and superlinear nonlinearity homogeneous Dirichlet boundary condition. Further, solution(s) will be proved bounded weak comparison principle has also been proved. A ‘\(C^1\) versus \(W_0^{s,p}\)’ analysis discussed.

The paper is devoted to the study of subdiffusion equations with Mittag-Leffler nonlinearity. The comparison principle proved in a bounded domain. results on local existence, global and blow-up solutions initial-boundary value problem are obtained. In addition, existence initial whole Euclidean space proven.