Showing papers in "Journal of Mathematical Analysis and Applications in 2001"

TL;DR: In this paper, the generalized Lebesgue spaces L-p(x)(Omega) and generalized lebesgue-Sobolev spaces W-m,W-p (x) were studied.

TL;DR: In this article, a Sobolev-type embedding theorem for generalized Lebesgue-Sobolev space Wk, p(x)(Ω), where Ω is an open domain in RN(N ≥ 2) with cone property, was given.

TL;DR: In this article, the dynamics of predator-prey models with the Beddington-DeAngelis functional response were analyzed from the viewpoint of permanence and extinction, and criteria for permanence were derived for systems without diffusion or with no-flux boundary conditions.

TL;DR: In this paper, a predator-prey system with one or two delays and a unique positive equilibrium is considered and its dynamics are studied in terms of the local stability of E∗ and of the description of the Hopf bifurcation that is proven to exist as one of the delays (taken as a parameter) crosses some critical values.

TL;DR: In this paper, the existence of a positive solution to the boundary value problem was shown if f is either superlinear or sublinear, by applying the fixed point theorem in cones.

TL;DR: In this paper, a linear operator is defined by means of the Hadamard product (or convolution) and two families of meromorphically multivalent functions are introduced and investigated.

TL;DR: In this article, sufficient and realistic conditions are obtained for the existence of positive periodic solutions for both periodic Lotka-Volterra equations and systems with distributed or state-dependent delays.

TL;DR: The aim of this paper is to outline a general theory of fuzzy closure operators and fuzzy closure systems, and to introduce the necessary concepts.

TL;DR: Ghosh and Debnath as mentioned in this paper proved sufficient and necessary conditions for Ishikawa iterative sequences of asymptotically quasi-nonexpansive mappings to converge to fixed points.

TL;DR: Rubinstein and Schatzman as discussed by the authors showed that the spectrum of the Neumann Laplacian on Me converges when e → 0 to the spectrum for an ODE problem on M. The results of this kind arise naturally in mesoscopic physics and other areas of physics and chemistry.

TL;DR: The notion of local fractional derivative introduced by Kolvankar and Gangal as discussed by the authors allows a fine study of the local structure of irregular (fractal) functions and extends classical theorems of analysis to non-differentiable functions.

TL;DR: In this article, the concept of τ-distance on a metric space was introduced, which is a generalized concept of both w -distance and Tataru's distance, and the relation between w-distance and τ -distance was discussed.

TL;DR: In this article, a semilinear partial differential equation of hyperbolic type with a convolution term describing simple viscoelastic materials with fading memory is considered, and the past history (memory) of the displacement as a new variable is transformed into a dynamical system in a suitable Hilbert space.

TL;DR: In this article, a singularly perturbed elliptic convection-diffusion problem on the unit square is considered, and a new asymptotic expansion of its solution is constructed, giving precise conditions under which the solution can be decomposed in a particularly opportune way into a sum of smooth and layer functions.

TL;DR: Oscillation criteria for nth order differential equations with deviating arguments of the form x (n − 1) ( t ) α − 1 x ( n − 1), (t ) + F(t, x[g(t)]) = 0, n even are established in this paper.

TL;DR: The existence and multiplicity of periodic solutions for non-autonomous second-order systems with locally coercive potential were shown in this paper. But their results were restricted to a subset of the positive-measure subset of [0, T ].

TL;DR: In this article, the existence of nontrivial solutions for the problem Δpu = |u|p − 2u in a bounded smooth domain Ω ⊂ RN, with a nonlinear boundary condition given by |∇u| p − 2∂u/∂ν = f(u) on the boundary of the domain was studied.

TL;DR: In this article, a generalization of the notion of p -invex sets with respect to η leads to a new class of functions, called (p, r )-pre-in-vex functions, and a family of real functions called, in general, (p, r ) − pre-invx functions with respect η (without differentiability) or ( p, r − v ) − v − invex (in the differentiable case) is introduced.

TL;DR: In this paper, the authors extend some compact imbedding theorems of Strauss-Lions type to the space W 1, Ω p ( x ) (Ω) when the domain has some symmetric properties and p( x ) satisfies some conditions.

TL;DR: In this article, a characterization of a preinvex function in terms of its relationship with an intermediate-point pre-vexity and prequasi-inveXity is provided.

TL;DR: In this article, the stability of a singular point for planar discontinuous differential equations with a line of discontinuities was studied, for the most generic cases, by computing some kind of Lyapunov constants.

TL;DR: In this article, a predator-prey model with a stage structure for the predator is proposed, which improves the assumption that each individual predator has the same ability to capture prey.

TL;DR: In this paper, a condition ensuring calmness of a class of multifunctions between finite-dimensional spaces is derived in terms of subdifferential concepts developed by Mordukhovich, which allows one to derive dual constraint qualifications in nonlinear optimization that are weaker than conventional ones but still sufficient for the existence of Lagrange multipliers.

TL;DR: In this article, the authors established maximal regularity of type Lp for a parabolic evolution equation u′(t) = ǫ(t), ∈ C([0, T], L (D(A(0)), X)) and constructed the corresponding evolution family on the underlying Banach space X. The results are applied to parabolic partial differential equations with continuous coefficients.

TL;DR: In this article, Morse theory and local linking are used to study the existence of multiple nontrivial solutions for a class of Dirichlet boundary value problems with double resonance at infinity and at 0.

TL;DR: In this article, a real q-uniformly smooth Banach space which is also uniformly convex (for example, Lp or lp spaces, 1) is considered.

TL;DR: In this paper, the weighted Hardy-Littlewood average of nonnegative functions ψ defined on [0, 1] is characterized for functions defined on the Euclidean plane.

TL;DR: With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of a delayed ratio-dependent predator-prey system in a periodic environment.