We study a nonlinear periodic problem driven by the p（t）-Laplacian and having a nonsmooth potential （hemivariational inequalities）. Using a variational method based on nonsmooth critical point theory for locally L...We study a nonlinear periodic problem driven by the p（t）-Laplacian and having a nonsmooth potential （hemivariational inequalities）. Using a variational method based on nonsmooth critical point theory for locally Lipschitz functions, we first prove the existence of at least two nontrivial solutions under the generalized subquadratic and then establish the existence of at least one nontrivial solution under the generalized superquadratic.展开更多
In this article, we investigate the existence of periodic solutions for a class of nonautonomous second-order differential systems with p(t)-Laplacian. Some multiplicity results are obtained by using critical point th...In this article, we investigate the existence of periodic solutions for a class of nonautonomous second-order differential systems with p(t)-Laplacian. Some multiplicity results are obtained by using critical point theory, which extend some known results.展开更多
This paper deals with the existence of solutions to the p（t）-Laplacian equation with four-point boundary conditions. It is shown, by Leray-Schauder fixed point theorem and degree method, that under suitable conditio...This paper deals with the existence of solutions to the p（t）-Laplacian equation with four-point boundary conditions. It is shown, by Leray-Schauder fixed point theorem and degree method, that under suitable conditions, solutions of the problem exist. The interesting point is that p（t） is a general function.展开更多
Supercritical carbon dioxide（SC-CO2 ） is considered in green chemistry as a substitute for conventional solvents in chemical reactions due to its environmentally benign character. Recently we have reported the homog...Supercritical carbon dioxide（SC-CO2 ） is considered in green chemistry as a substitute for conventional solvents in chemical reactions due to its environmentally benign character. Recently we have reported the homogeneous hydroformylation of propylene in supercritical carbon dioxide（ SC-CO2 ） , which is an example of this kind of application of carbon dioxide. The determination for the critical parameters of carbon dioxide ＋ butyraldehyde mixtures is necessary for this reaction design which is the focus of the present paper. The critical parameters of the binary systems were determined via the static visual method at a constant volume with the molar fraction of butyraldehyde ranging from 1.0% to 2. 2% and the pressure ranging from 5 to 10 MPa. The experimental results show that the critical pressure and temperature increased with increasing the molar fraction of butyraldehyde. The bubble（dew） temperatures and the bubble （dew） pressures for the binary systems were also determined experimentally. The p-T Figures at different compositions of the binary systems were described. In addition, the critical compressibility factors Zc of the binary systems at different concentrations of n-butyraldehyde were calculated. It was found that the critical compressibility factor values of the binary systems decreased with increasing the molar fraction of n-butyraldehyde in the experimental range.展开更多
基金supported by the National Science Foundation of China (11001063, 10971043)the Fundamental Research Funds for the Central Universities (HEUCF 20111134)+2 种基金China Postdoctoral Science Foundation Funded Project (20110491032)Heilongjiang Provincial Science Foundation for Distinguished Young Scholars (JC200810)Program of Excellent Team in Harbin Institute of Technology and the Natural Science Foundation of Heilongjiang Province (A200803)
文摘We study a nonlinear periodic problem driven by the p（t）-Laplacian and having a nonsmooth potential （hemivariational inequalities）. Using a variational method based on nonsmooth critical point theory for locally Lipschitz functions, we first prove the existence of at least two nontrivial solutions under the generalized subquadratic and then establish the existence of at least one nontrivial solution under the generalized superquadratic.
基金Supported by the Natural Science Foundation of Anhui Province（1408085MA02, 1208085 MA13, 1308085MA01, 1308085QA15） Supported by the Key Foundation of Anhui Education Bureau （KJ2012A019, KJ2013A028）+2 种基金 Supported by the National Natural Science Foundation of China（11271371, 11301 004） Supported by the Research Fund for the Doctoral Program of Higher Education（20113401110001） Supported by 211 Project of Anhui University（02303129, 02303303-33030011, 02303902-39020011, KYXL2012004 XJYJXKC04, yfcl00012）
文摘In this article, we investigate the existence of periodic solutions for a class of nonautonomous second-order differential systems with p(t)-Laplacian. Some multiplicity results are obtained by using critical point theory, which extend some known results.
基金Supported by the National Natural Science Foundation of China (11761038)Science and Technology Project of Department of Education of Jiangxi Province (GJJ180583)。
基金supported by Anhui Provincial Nature Science Foundation(1208085MA13)the Research Fund for the Doctoral Program of Higher Education(20103401120002,20113401120001)+1 种基金211 Project of Anhui University(02303129,KJTD002B,02303303-33030011,02303902-39020011)the Key Foundation of Anhui Education Bureau(KJ2012A019)
基金The NSF(11271154)of Chinathe Key Lab of Symbolic Computation and Knowledge Engineering of Ministry of Education+1 种基金the 985 program of Jilin Universitythe DR Fund(150152)of Henan University of Technology
文摘This paper deals with the existence of solutions to the p（t）-Laplacian equation with four-point boundary conditions. It is shown, by Leray-Schauder fixed point theorem and degree method, that under suitable conditions, solutions of the problem exist. The interesting point is that p（t） is a general function.
文摘Supercritical carbon dioxide（SC-CO2 ） is considered in green chemistry as a substitute for conventional solvents in chemical reactions due to its environmentally benign character. Recently we have reported the homogeneous hydroformylation of propylene in supercritical carbon dioxide（ SC-CO2 ） , which is an example of this kind of application of carbon dioxide. The determination for the critical parameters of carbon dioxide ＋ butyraldehyde mixtures is necessary for this reaction design which is the focus of the present paper. The critical parameters of the binary systems were determined via the static visual method at a constant volume with the molar fraction of butyraldehyde ranging from 1.0% to 2. 2% and the pressure ranging from 5 to 10 MPa. The experimental results show that the critical pressure and temperature increased with increasing the molar fraction of butyraldehyde. The bubble（dew） temperatures and the bubble （dew） pressures for the binary systems were also determined experimentally. The p-T Figures at different compositions of the binary systems were described. In addition, the critical compressibility factors Zc of the binary systems at different concentrations of n-butyraldehyde were calculated. It was found that the critical compressibility factor values of the binary systems decreased with increasing the molar fraction of n-butyraldehyde in the experimental range.
