There recently has been much interest in non-interior continuation/smoothingmethods for solving linear/nonlinear complementarity problems. We describe extensions of such methods to complementarity problems defined over the cone of block-diagonal symmetric positive semidefinite real matrices. These extensions involve the ChenMangasarian class of smoothing functions and the smoothed Fischer-Burme...

In this paper, we study φ-Laplacian problems for differential inclusions with Dirichlet boundary conditions. We prove the existence of solutions under both convexity and nonconvexity conditions on the multivalued right-hand side. The nonlinearity satisfies either a Nagumotype growth condition or an integrably boundedness one. The proofs rely on the Bonhnenblust-Karlin fixed point theorem and th...

This paper is concerned with the following Schrödinger equation: { − u+ V (x)u = f(x, u), for x ∈ R , u(x) → 0, as |x| → ∞, where the potential V and f are periodic with respect to x and 0 is a boundary point of the spectrum σ(− + V ). By a new technique for showing the boundedness of Cerami sequences, we are able to obtain the existence of nontrivial solutions with mild assumptions on f .

In this paper, we propose an epidemic model with age-dependence vaccination, latency and relapse. We derive the positivity and boundedness of solutions and find the basic reproduction number. Asymptotic smoothness, the existence of global compact attractor and uniform persistence of the model are investigated. By constructing Lyapunov functionals, we establish global stability of the equilibria...

We investigate control systems as variational equations in non-standard chains of rigged Hilbert spaces. Monotonicity properties of nonlinearities are introduced with respect to such riggings generated by Lyapunov operators and invariant cones. Sufficient frequency domain conditions for boundedness and the existence of Bohr and Stepanov almost periodic solutions are derived. As an example we co...

With the help of the continuation theorem of the coincidence degree, a priori estimates, and differential inequalities, we make a further investigation of a class of planar systems, which is generalization of some existing neural networks under a time-varying environment. Without assuming the smoothness, monotonicity, and boundedness of the activation functions, a set of sufficient conditions i...

In this paper, a non-linear mathematical model is proposed to study the dynamics of a disease transmission among the prey population. The model includes the harvesting of infected prey. The existence, uniqueness and boundedness of the solution of the model are investigated. The feasibility and the stability conditions of the fixed points of the system are analyzed by applying linearization meth...

In this paper, the existence theorems of solutions for generalized weak vector equilibrium problems are developed in real reflexive Banach spaces. Based on recession method and scalarization technique, we derive a characterization of nonemptiness and boundedness of solution set for generalized weak vector equilibrium problems. Moreover, Painlevé-Kuratowski upper convergence of solution set is a...

A stochastic non-autonomous predator-prey system with Beddington-DeAngelis functional response is proposed, the existence of a global positive solution and stochastically ultimate boundedness are derived. Sufficient conditions for extinction, non-persistence in the mean, weak persistence in the mean and strong persistence in the mean are established. The global attractiveness of the solution is...