In this paper, we consider the Cauchy problem of degenerate parabolic equation not in divergence form u, = uPAu ＋ uq, p 〉 1, q 〉 1, and give the blow-up conditions and the critical Fujita exponents for the existenc...In this paper, we consider the Cauchy problem of degenerate parabolic equation not in divergence form u, = uPAu ＋ uq, p 〉 1, q 〉 1, and give the blow-up conditions and the critical Fujita exponents for the existence of global and non-global solutions to the Cauchy problem.展开更多
In this paper,the existence,the uniqueness,the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation ut-αuxx...In this paper,the existence,the uniqueness,the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation ut-αuxx-βuxxt=F（u）-βF （u）xx are proved,where α,β 0 are constants,F（s） is a given function.展开更多
The existence of positive solutions is investigated for following semipositone nonlinear third-order three-point BVP ω''(t) - λf(t,w(t)) = 0, 0 ≤ t ≤ 1, ω(0) = ω'(n) = ω'(1) = 0.
This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic hemivariational inequalities. The unknown coefficient of elliptic hemivariational inequalities depends on the gradient of the sol...This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic hemivariational inequalities. The unknown coefficient of elliptic hemivariational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic hemivariational inequalities are uniquely solvable for the given class of coefficients. The result of existence of quasisolutions of the inverse problems is obtained.展开更多
This paper discusses a problem of optimal tracking for a linear control system driven by fractional Brownian motion.An equation is obtained for the linear Markov feedback control.The existence and uniqueness of the so...This paper discusses a problem of optimal tracking for a linear control system driven by fractional Brownian motion.An equation is obtained for the linear Markov feedback control.The existence and uniqueness of the solution to the equation are also studied.展开更多
In this paper,we consider the existence of positive solutions for the singular fourth-order four point boundary value problem with p-Laplacian operator.By using the fixed point theorem of cone expansion and compressio...In this paper,we consider the existence of positive solutions for the singular fourth-order four point boundary value problem with p-Laplacian operator.By using the fixed point theorem of cone expansion and compression,the existence of multiple positive solutions is ob-tained.展开更多
By constructing a special cone and applying the fixed point theorem of cone compression and expansion,this paper investigates the existence of positive solutions for a class of first order singular boundary value prob...By constructing a special cone and applying the fixed point theorem of cone compression and expansion,this paper investigates the existence of positive solutions for a class of first order singular boundary value problem(BVP,for short) on unbounded domains.Moreover,an incomparable result about two positive solutions for the BVP is also obtained and an example is given to illustrate the application of the main results.展开更多
文摘In this paper, we consider the Cauchy problem of degenerate parabolic equation not in divergence form u, = uPAu ＋ uq, p 〉 1, q 〉 1, and give the blow-up conditions and the critical Fujita exponents for the existence of global and non-global solutions to the Cauchy problem.
基金Supported by the National Natural Science Foundation of China（10671182）
文摘In this paper,the existence,the uniqueness,the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation ut-αuxx-βuxxt=F（u）-βF （u）xx are proved,where α,β 0 are constants,F（s） is a given function.
基金supported by the National Natural Science Foundation of China(No.10971019)the GuangxiProvincial Natural Science Foundation of China(No.2010GXNSFA013114)
文摘This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic hemivariational inequalities. The unknown coefficient of elliptic hemivariational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic hemivariational inequalities are uniquely solvable for the given class of coefficients. The result of existence of quasisolutions of the inverse problems is obtained.
基金partially supported by a grant from the Simons Foundation #209206
文摘This paper discusses a problem of optimal tracking for a linear control system driven by fractional Brownian motion.An equation is obtained for the linear Markov feedback control.The existence and uniqueness of the solution to the equation are also studied.
基金the National Natural Science Foundation of China (No.10671181)
文摘In this paper,we consider the existence of positive solutions for the singular fourth-order four point boundary value problem with p-Laplacian operator.By using the fixed point theorem of cone expansion and compression,the existence of multiple positive solutions is ob-tained.
基金Foundation item： the National Natural Science Foundation of China （No. 10671167） the Natural Science Foundation of Liaocheng University （No. 31805）.
文摘By constructing a special cone and applying the fixed point theorem of cone compression and expansion,this paper investigates the existence of positive solutions for a class of first order singular boundary value problem(BVP,for short) on unbounded domains.Moreover,an incomparable result about two positive solutions for the BVP is also obtained and an example is given to illustrate the application of the main results.
