Extremal values of half-eigenvalues for -Laplacian with weights in balls.
Various half-eigenvalues of scalar -Laplacian with indefinite integrable weights.
On an open problem of integral inequalities.
On a conjecture of Qi-type integral inequalities.
The stability of Ritz-Volterra projection and error estimates for finite element methods for a class of integro-differential equations of parabolic type
In this paper we first study the stability of Ritz-Volterra projection (see below) and its maximum norm estimates, and then we use these results to derive some error estimates for finite element methods for parabolic integro-differential equations.
On the extended Hardy's inequality.
Multi-point boundary value problems for higher order differential equations.
Existence criteria for singular boundary value problems with -Laplacian operators.
Defect correction and a posteriori error estimation of Petrov-Galerkin methods for nonlinear Volterra integro-differential equations
We present two defect correction schemes to accelerate the Petrov-Galerkin finite element methods [19] for nonlinear Volterra integro-differential equations. Using asymptotic expansions of the errors, we show that the defect correction schemes can yield higher order approximations to either the exact solution or its derivative. One of these schemes even does not impose any extra regularity requirement on the exact solution. As by-products, all of these higher order numerical methods can also be...
Numerical solutions for second-kind Volterra integral equations by Galerkin methods
In this paper, we study the global convergence for the numerical solutions of nonlinear Volterra integral equations of the second kind by means of Galerkin finite element methods. Global superconvergence properties are discussed by iterated finite element methods and interpolated finite element methods. Local superconvergence and iterative correction schemes are also considered by iterated finite element methods. We improve the corresponding results obtained by collocation methods in the recent...
Global existence of periodic solutions in a simplified four-neuron BAM neural network model with multiple delays.
Stability and bifurcation in a simplified four-neuron bam neural network with multiple delays.
Global asymptotic stability of 3-species mutualism models with diffusion and delay effects.
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