Transition layers arising from square-wave-like periodic solutions of a singularly perturbed delay differential equation are studied. Such transition layers correspond to heteroclinic orbits connecting a pair of equilibria of an associated system of transition layer equations. Assuming a monotonicity condition in the nonlinearity, we prove these transition layer equations possess a unique heter...

To minimize the primal support vector machine (SVM) problem, we propose to use iterative majorization. To do so, we propose to use iterative majorization. To allow for nonlinearity of the predictors, we use (non)monotone spline transformations. An advantage over the usual kernel approach in the dual problem is that the variables can be easily interpreted. We illustrate this with an example from...

The full history recursive multilevel Picard approximation method for semilinear parabolic partial differential equations (PDEs) is the only which provably overcomes curse of dimensionality general time horizons if coefficient functions and nonlinearity are globally Lipschitz continuous gradient-independent. In this article we extend result to locally monotone functions. Our results cover a ran...

In this paper we prove the existence and approximation of solution for a nonlinear two point boundary value problem ordinary second order hybrid differential equations with Dirichlet conditions via construction an algorithm solution. The nonlinearity present on right hand side equation is assumed to be Caratho\`eodory proof based monotone iteration method Dhage (2014) in ordered Banach space.

We study a Dirichlet optimal control problem for a quasi-linear monotone elliptic equation, the so-called weighted p-Laplace problem. The coefficient of the p-Laplacian, the weight u, we take as a control in BV (Ω) ∩ L∞(Ω). In this article, we use box-type constraints for the control such that there is a strictly positive lower and some upper bound. In order to handle the inherent degeneracy of...

We consider two singular limits: a fast reaction limit with non-monotone nonlinearity and regularization of the forward-backward diffusion equation. derive pointwise identities satisfied by Young measure generated these problems. As result, we obtain an explicit formula for even without non-degeneracy assumption used in previous works. The main new idea is application Radon–Nikodym theorem to d...

We prove the existence of reaction-diffusion traveling fronts in mean zero space-time periodic shear flows for nonnegative reactions including the classical KPP (Kolmogorov-Petrovsky-Piskunov) nonlinearity. For the KPP nonlinearity, the minimal front speed is characterized by a variational principle involving the principal eigenvalue of a space-time periodic parabolic operator. Analysis of the ...

Combined with all density-dependent factors, the per capita growth rate of a species may be nonmonotonic. One important consequence is that species may suffer from weak Allee effects or strong Allee effects. In this paper, we study the permanence of a discrete-time two-species-interaction model with non-monotonic per capita growth rates for the first time. By using the average Lyapunov function...

Lifting is a procedure for deriving strong valid inequalities for a closed set from inequalities that are valid for its lower dimensional restrictions. It is arguably one of the most effective ways of strengthening linear programming relaxations of 0–1 programming problems. Wolsey (1977) and Gu et al. (2000) show that superadditive lifting functions lead to sequence independent lifting of valid...

We introduce a new concept of general $G$-$eta$-monotone operator generalizing the general $(H,eta)$-monotone operator cite{arvar2, arvar1}, general $H-$ monotone operator cite{xiahuang} in Banach spaces, and also generalizing $G$-$eta$-monotone operator cite{zhang}, $(A, eta)$-monotone operator cite{verma2}, $A$-monotone operator cite{verma0}, $(H, eta)$-monotone operator cite{fanghuang}...