Nonlinear delay Caputo fractional differential equations with non-instantaneous impulses are studied and we consider the general case of delay,depending on both the time and the state variable.The case when the lower ...Nonlinear delay Caputo fractional differential equations with non-instantaneous impulses are studied and we consider the general case of delay,depending on both the time and the state variable.The case when the lower limit of the Caputo fractional derivative is fixed at the initial time,and the case when the lower limit of the fractional derivative is changed at the end of each interval of action of the impulse are studied.Practical stability properties,based on the modified Razumikhin method are investigated.Several examples are given in this paper to illustrate the results.展开更多
A new upper and lower solution theory is presented for the second order problem （G＇（y））＇＋ f（t, y） = 0 on finite and infinite intervals. The theory on finite intervals is based on a Leray-Schauder alternative,...A new upper and lower solution theory is presented for the second order problem （G＇（y））＇＋ f（t, y） = 0 on finite and infinite intervals. The theory on finite intervals is based on a Leray-Schauder alternative, where as the theory on infinite intervals is based on results on the finite interval and a diagonalization process.展开更多
This paper discusses both the nonexistence of positive solutions for second-order three-point boundary value problems when the nonlinear term f（t, x, y） is superlinear in y at y = 0 and the existence of multiple pos...This paper discusses both the nonexistence of positive solutions for second-order three-point boundary value problems when the nonlinear term f（t, x, y） is superlinear in y at y = 0 and the existence of multiple positive solutions for second-order three-point boundary value problems when the nonlinear term f（t, x,y） is superlinear in x at ＋∞.展开更多
We establish new criteria for the existence of either positive or nonzero solutions of the Urysohn integral equation. We also discuss the existence of an interval of positive eigenvalues and sufficient conditions for ...We establish new criteria for the existence of either positive or nonzero solutions of the Urysohn integral equation. We also discuss the existence of an interval of positive eigenvalues and sufficient conditions for the existence of at least a positive eigenvalue with a nonzero or positive eigenfunction for the Urysohn integral operator. Among others, we employ techniques based on fixed point index theory for compact maps, which are new for this type of equation.展开更多
Some coincidence point theorems satisfying a general contractive condition are proved. As applications, some invariant approximation results are also obtained and several related results in the literature are either e...Some coincidence point theorems satisfying a general contractive condition are proved. As applications, some invariant approximation results are also obtained and several related results in the literature are either extended or improved.展开更多
New oscillation criteria for general differential equations of the form x^（n）（t）＋pn-1 （t）x^（n-1）（t）＋…＋P1（t）x′（t）＋p0（t）x（t）＋q1（t）x^μ （t） = q2 （t）x^λ （t）＋e（t） where λ,μ are the ra...New oscillation criteria for general differential equations of the form x^（n）（t）＋pn-1 （t）x^（n-1）（t）＋…＋P1（t）x′（t）＋p0（t）x（t）＋q1（t）x^μ （t） = q2 （t）x^λ （t）＋e（t） where λ,μ are the ratios of positive odd integers, 0 〈 μ 〈 1 and λ 〉 1 are established.展开更多
基金supported by Portuguese funds through the CIDMA-Center for Research and Development in Mathematics and Applicationsthe Portuguese Foundation for Science and Technology(FCT-Fundação para a Ciência e a Tecnologia),within project UIDB/04106/2020Fund Scientific Research MU21FMI007,University of Plovdiv"Paisii Hilendarski".
文摘Nonlinear delay Caputo fractional differential equations with non-instantaneous impulses are studied and we consider the general case of delay,depending on both the time and the state variable.The case when the lower limit of the Caputo fractional derivative is fixed at the initial time,and the case when the lower limit of the fractional derivative is changed at the end of each interval of action of the impulse are studied.Practical stability properties,based on the modified Razumikhin method are investigated.Several examples are given in this paper to illustrate the results.
基金Supported by Grant No.201/01/1451 of the Grant Agency of Czech Republicthe Council of Czech Government J14/98:153100011
文摘A new upper and lower solution theory is presented for the second order problem （G＇（y））＇＋ f（t, y） = 0 on finite and infinite intervals. The theory on finite intervals is based on a Leray-Schauder alternative, where as the theory on infinite intervals is based on results on the finite interval and a diagonalization process.
基金Supported by the National Natural Science Foundation of China(No.10571111)the fund of Shandong Education Committee(J07WH08).
文摘This paper discusses both the nonexistence of positive solutions for second-order three-point boundary value problems when the nonlinear term f（t, x, y） is superlinear in y at y = 0 and the existence of multiple positive solutions for second-order three-point boundary value problems when the nonlinear term f（t, x,y） is superlinear in x at ＋∞.
基金The first and third authors have been supported in part by Ministerio de Cienciay Tecnología(Spain)MTM2004-06652-C03-03
文摘We establish new criteria for the existence of either positive or nonzero solutions of the Urysohn integral equation. We also discuss the existence of an interval of positive eigenvalues and sufficient conditions for the existence of at least a positive eigenvalue with a nonzero or positive eigenfunction for the Urysohn integral operator. Among others, we employ techniques based on fixed point index theory for compact maps, which are new for this type of equation.
文摘Some coincidence point theorems satisfying a general contractive condition are proved. As applications, some invariant approximation results are also obtained and several related results in the literature are either extended or improved.
文摘New oscillation criteria for general differential equations of the form x^（n）（t）＋pn-1 （t）x^（n-1）（t）＋…＋P1（t）x′（t）＋p0（t）x（t）＋q1（t）x^μ （t） = q2 （t）x^λ （t）＋e（t） where λ,μ are the ratios of positive odd integers, 0 〈 μ 〈 1 and λ 〉 1 are established.
