In this paper, we prove the existence and uniqueness of a nonlinear perturbed stochastic fractional integro-differential equation of Volterra-Itô type involving nonlocal initial condition by using the theory of admissibility of integral operator and Banach fixed-point principle. Also the stability and boundedness of the second moments of the stochastic solution are studied. In addition, an appl...

We establish the existence and uniqueness of weak solution of the three-dimensional nonhomogeneous stationary Oseen flow around a rotating body in an exterior domain. This article is extension of the previous results on the whole space. For the present extension to the case of exterior domains, we will use the localization procedure (see e.g. KoSo). In this way we combine the previous results (...

Using the homotopy invariance property of the degree and a newly introduced concept of the interior-point-ε-exceptional family for continuous functions, we prove an alternative theorem concerning the existence of a certain interior-point of a continuous complementarity problem. Based on this result, we develop several sufficient conditions to assure some desirable properties (nonemptyness, boun...

In this paper, we propose a sufficient condition for the existence of solutions to general variational inequality problems (GV I(K,F , g)). The condition is also necessary when F is a g-P ∗ function. We also investigate the boundedness of the solution set of (GV I(K,F, g)). Furthermore, we show that when F is norm-coercive, the general complementarity problems (GCP (K,F, g)) has a nonempty comp...

This paper proves the global existence and boundedness of solutions to a general reaction–diffusion predator–prey system with prey-taxis defined on a smooth bounded domain with no-flux boundary condition. The result holds for domains in arbitrary spatial dimension and small prey-taxis sensitivity coefficient. This paper also proves the existence of a global attractor and the uniform persistence...

This paper deals with a Holling type III diffusive predator-prey model with stage structure and nonlinear density restriction in the space R. We first consider the asymptotical stability of equilibrium points for the model of ODE type. Then, the existence and uniform boundedness of global solutions and stability of the equilibrium points for the model of weakly coupled reactiondiffusion type ar...

We study the existence of periodic solutions for a class of quasi-parabolic equations involving the p-Laplacian (or any other nonlinear operators of similar class) perturbed by nonlinear terms and forced by rather irregular periodic in time excitations (including what we call abrupt changes). These equations may model problems for which, aside from the presence of the kind of nonlinear dissipat...

We study qualitative and quantitative properties of local weak solutions of the fast p-Laplacian equation, ∂tu = ∆pu, with 1 < p < 2. Our main results are quantitative positivity and boundedness estimates for locally defined solutions in domains of R× [0, T ]. We combine these lower and upper bounds in different forms of intrinsic Harnack inequalities, which are new in the very fast diffusion r...

−ε2∆u + V (x)u + ψu = f(u) in R, −ε2∆ψ = u in R, u > 0, u ∈ H(R), has been studied extensively, where the assumption for f(u) is that f(u) ∼ |u|p−2u with 4 < p < 6 and satisfies the Ambrosetti–Rabinowitz condition which forces the boundedness of any Palais– Smale sequence of the corresponding energy functional of the equation. The more difficult critical case is studied in this paper. As g(u) :...