This paper is devoted to demonstrating several multiplicity results of nontrivial weak solutions to double phase problems of Kirchhoff type with Hardy potentials.The main features of the paper are the appearance of no...This paper is devoted to demonstrating several multiplicity results of nontrivial weak solutions to double phase problems of Kirchhoff type with Hardy potentials.The main features of the paper are the appearance of non-local Kirchhoff coefficients and the Hardy potential,the absence of the compactness condition of Palais-Smale,and the L^(∞)-bound for any possible weak solution.To establish multiplicity results,we utilize the fountain theorem and the dual fountain theorem as main tools.Also,we give the L^(∞)-bound for any possible weak solution by exploiting the De Giorgi iteration method and a truncated energy technique.As an application,we give the existence of a sequence of infinitely many weak solutions converging to zero in L^(∞)-norm.To derive this result,we employ the modified functional method and the dual fountain theorem.展开更多
The principal resonance of Duffing random external excitation was investigated. oscillator to combined deterministic and The random excitation was taken to be white noise or harmonic with separable random amplitude an...The principal resonance of Duffing random external excitation was investigated. oscillator to combined deterministic and The random excitation was taken to be white noise or harmonic with separable random amplitude and phase. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The one peak probability density function of each of the two stable stationary solutions was calculated by the linearization method. These two one-peak-density functions were combined using the probability of realization of the two stable stationary solutions to obtain the double peak probability density function. The theoretical analysis are verified by numerical results.展开更多
A double-shell model of hydroelectric-generator stator system was established. Applying the theory of mechano-electric analytical dynamics theory, the nonlinear vibration equation of magnetism and solid coupling of hy...A double-shell model of hydroelectric-generator stator system was established. Applying the theory of mechano-electric analytical dynamics theory, the nonlinear vibration equation of magnetism and solid coupling of hydroelectric-generator stator system, under steadily balanced three-phases operating condition, was obtained. According to the method of multiple scales for nonlinear oscillations, the double resonances of magnetism and solid coupling of hydroelectric-generator stater system, were investigated. It is pointed out that the system has abundant dynamics phenomenon including the attendant jumps and coexistence of multiple stable motions.展开更多
The aim of this paper is the study of a double phase problems involving superlinear nonlinearities with a growth that need not satisfy the Ambrosetti-Rabinowitz condition.Using variational tools together with suitable...The aim of this paper is the study of a double phase problems involving superlinear nonlinearities with a growth that need not satisfy the Ambrosetti-Rabinowitz condition.Using variational tools together with suitable truncation and minimax techniques with Morse theory,the authors prove the existence of one and three nontrivial weak solutions,respectively.展开更多
An analytical method is introduced to investigate double Hopf bifurcations induced by two delays qualitatively and quantitatively.As an illustrative example,the clear procedure is demonstrated to study delay-induced w...An analytical method is introduced to investigate double Hopf bifurcations induced by two delays qualitatively and quantitatively.As an illustrative example,the clear procedure is demonstrated to study delay-induced weak resonant double Hopf bifurcation in a nonlinear system with multiple delays.When two delays are close to double Hopf bifurcation point,all solutions derived from the bifurcation are classified qualitatively and expressed explicitly.Numerical simulations are a good agreement with our theoretical analysis,and also already work in references.The results show that our work in this paper proposes a simple and valid method for investigating delay-induced double Hopf bifurcations.The important feature of our work is that the explicit expression of periodic solutions is easy to be obtained by solving algebraic equations.展开更多
文摘This paper is devoted to demonstrating several multiplicity results of nontrivial weak solutions to double phase problems of Kirchhoff type with Hardy potentials.The main features of the paper are the appearance of non-local Kirchhoff coefficients and the Hardy potential,the absence of the compactness condition of Palais-Smale,and the L^(∞)-bound for any possible weak solution.To establish multiplicity results,we utilize the fountain theorem and the dual fountain theorem as main tools.Also,we give the L^(∞)-bound for any possible weak solution by exploiting the De Giorgi iteration method and a truncated energy technique.As an application,we give the existence of a sequence of infinitely many weak solutions converging to zero in L^(∞)-norm.To derive this result,we employ the modified functional method and the dual fountain theorem.
基金Project supported by the National Natural Science Foundation of China (Key Program) (No.10332030)the Natural Science Foundation of Guangdong Province of China (No.04011640)
文摘The principal resonance of Duffing random external excitation was investigated. oscillator to combined deterministic and The random excitation was taken to be white noise or harmonic with separable random amplitude and phase. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The one peak probability density function of each of the two stable stationary solutions was calculated by the linearization method. These two one-peak-density functions were combined using the probability of realization of the two stable stationary solutions to obtain the double peak probability density function. The theoretical analysis are verified by numerical results.
文摘A double-shell model of hydroelectric-generator stator system was established. Applying the theory of mechano-electric analytical dynamics theory, the nonlinear vibration equation of magnetism and solid coupling of hydroelectric-generator stator system, under steadily balanced three-phases operating condition, was obtained. According to the method of multiple scales for nonlinear oscillations, the double resonances of magnetism and solid coupling of hydroelectric-generator stater system, were investigated. It is pointed out that the system has abundant dynamics phenomenon including the attendant jumps and coexistence of multiple stable motions.
基金supported by the National Natural Science Foundation of China (No. 11201095)the Fundamental Research Funds for the Central Universities (No. 3072022TS2402)+1 种基金the Postdoctoral research startup foundation of Heilongjiang (No. LBH-Q14044)the Science Research Funds for Overseas Returned Chinese Scholars of Heilongjiang Province (No. LC201502)
文摘The aim of this paper is the study of a double phase problems involving superlinear nonlinearities with a growth that need not satisfy the Ambrosetti-Rabinowitz condition.Using variational tools together with suitable truncation and minimax techniques with Morse theory,the authors prove the existence of one and three nontrivial weak solutions,respectively.
基金supported by the National Natural Science Foundation of China(Grant Nos.11872175,11572224,61603125 and 21130010)Young Talents Fund of Henan University of Economics and Law+1 种基金National Key Project Cultivation Project of Henan University of Economics and LawKey Research Project of Higher Education Institutions of Henan Province(Grant No.18A110003)。
文摘An analytical method is introduced to investigate double Hopf bifurcations induced by two delays qualitatively and quantitatively.As an illustrative example,the clear procedure is demonstrated to study delay-induced weak resonant double Hopf bifurcation in a nonlinear system with multiple delays.When two delays are close to double Hopf bifurcation point,all solutions derived from the bifurcation are classified qualitatively and expressed explicitly.Numerical simulations are a good agreement with our theoretical analysis,and also already work in references.The results show that our work in this paper proposes a simple and valid method for investigating delay-induced double Hopf bifurcations.The important feature of our work is that the explicit expression of periodic solutions is easy to be obtained by solving algebraic equations.
