SECOND ORDER BVPS ON THE REAL LINE This paper is concerned with the solvability of a second-order integro-differential equation with Dirichlet boundary conditions on the real line. Under some conditions on the real parameters and coefficients, some existence results are presented. We mainly use fixed point arguments.
SOLUTION TO p(x)-LAPLACIAN PROBLEM WITH HARDY TERM We study the existence of solutions to a class of p(x)-Laplacian equations involving singular Hardy terms for nonlinear terms of the type f(x, t) = ±(-λ|t|m(x)-2t +|t|q(x)-2t). First we show the existence of infinitely many weak solutions for anyλ > 0, and next prove that if λ is large enough then there exists a nontrivial weak solution. Our approach relies on direct variational methods and the theory of variable exponent Lebesgue-Sobolev spaces.
ON THE OSCILLATION OF CERTAIN SECOND ORDER QUASILINEAR NEUTRAL DIFFERENTIAL EQUATIONS Some new oscillation theorems for a second order superlinear-sublinear neutral differential equation are established under some conditions. Our results improve and extend the main results in the previous literature. Explicit examples related to the main results are given.
OSCILLATION OF CERTAIN EVEN ORDER NONLINEAR PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE In this paper, the oscillation of a class of nonlinear even order neutral partial functional differential equations with continuous distributed delay is studied. By employing the generalized Riccati transformation and the technique of differential inequalities, some new sufficient conditions are obtained for the oscillation of the partial differential equations under Robin boundary value conditions. The results generalize some of the previous results.
TRIPLE POSITIVE SOLUTIONS TO A CLASS OF NONLINEAR BEAM EQUATIONS In this paper, an existence criterion of triple positive solutions to a class of nonlinear beam equations is established using the Leggett-Williams fixed point theorem.An example is also included to demonstrate the result. The interesting point is that the nonlinear term is involved with all low-level derivatives.
EXTINCTION IN A GILPIN-AYALA COMPETITION SYSTEM WITH THE EFFECT OF TOXIC SUBSTANCES In this paper,we consider a two dimensional Gilpin-Ayala competition system with the effect of toxic substances.We prove that one of components is driven to extinction while the other one is stable under some conditions.As a result,we generalize the previous results.
SOME PROPERTIES OF GENERALIZED SOLUTIONS TO QUASILINEAR ELLIPTIC EQUATIONS In this paper, we introduce quasilinear elliptic equations in divergent form. It is permitted that the growth orders of A(x, u, ζ) and B(x, u, ζ) with respect to u arrive at the critical exponents and the growth order of B(x, u, ζ) with respect to ζ is supercritical. Many aspects can be solved satisfactorily.
POSITIVE SOLUTIONS TO FOURTH-ORDER THREE-POINT NONLINEAR EIGENVALUE PROBLEM In this paper, we investigate a fourth-order three-point nonlinear eigenvalue problem. By the Krasnosel’skii’s fixed-point theorem in cone, some new results on the existence of positive solutions are obtained.
SOME NEW GENERALIZED RETARDED NONLINEAR INTEGRAL INEQUALITIES WITH APPLICATIONS Some new generalized retarded nonlinear integral inequalities are discussed and upper bound estimations of unknown functions are given by adapting novel analysis techniques. These estimations can be applied to study differential-integral equations and some practical problems in engineering.
APPLICATIONS OF NONLINEAR MEASURE ABOUT l~2-NORM TO SYNCHRONIZATION ANALYSIS OF COMPLEX NETWORKS VIA THE GENERAL INTERMITTENT CONTROL Based on the nonlinear measure about /-norm,a novel and effective approach is applied to estimate the scope of state vectors of dynamic systems.By the general intermittent control,some simple yet generic criteria are derived ensuring the exponential stability of dynamic systems.The numerical simulations,whose theoretical results are applied to robust synchronization of complex networks,demonstrate the effectiveness and feasibility of the proposed technique.
INFORMATION FOR AUTHORS <正>Submission of manuscripts Annals of Applied Mathematics(The original name is Annals of Differential Equations,which was founded in 1985)is an international journal devoted to the publication of original research papers and review articles in all areas of applied mathematics,with