We propose a regular spherically symmetric spacetime solution with three parameters in Einstein gravity coupled to nonlinear electrodynamics(NED), which describes the NED black hole with electric charge. It is found t...We propose a regular spherically symmetric spacetime solution with three parameters in Einstein gravity coupled to nonlinear electrodynamics(NED), which describes the NED black hole with electric charge. It is found that the system enclosed by the horizon of NED spacetime satisfies the first law of thermodynamics. In order to obtain the NED spacetime with only electric charge, the case of two parameters taking the same value is considered. In this case, we express the mass of the NED spacetime as a function of the entropy and electric charge of the NED black hole, give the Smarr-like formula and the approximate Smarr formula for the mass of NED spacetime.展开更多
This paper is concerned with the connection between the Volterra series and the regular perturbation method in nonlinear systems analyses. It is revealed for the first time that, for a forced polynomial nonlinear syst...This paper is concerned with the connection between the Volterra series and the regular perturbation method in nonlinear systems analyses. It is revealed for the first time that, for a forced polynomial nonlinear system, if its derived linear system is a damped dissipative system, the steady response obtained through the regular perturbation method is exactly identical to the response given by the Volterra series. On the other hand, if the derived linear system is an undamped conservative system, then the Volterra series is incapable of modeling the forced polynomial nonlinear system. Numerical examples are further presented to illustrate these points. The results provide a new criterion for quickly judging whether the Volterra series is applicable for modeling a given polynomial nonlinear system.展开更多
We consider a parametric Dirichlet problem driven by the p-Laplacian with a Caratheodory reaction of equidiffusive type. Our hypotheses incorporate as a special case the equidiffusive p-logistic equation. We show that...We consider a parametric Dirichlet problem driven by the p-Laplacian with a Caratheodory reaction of equidiffusive type. Our hypotheses incorporate as a special case the equidiffusive p-logistic equation. We show that if λ1 〉 0 is the principal eigenvalue of the Dirichlet negative p-Laplacian and ）λ 〉 λ1 （/k being the parameter）, the problem has a unique positive solution, while for ）λ ∈ （0, λ1], the problem has no positive solution.展开更多
We consider a nonlinear Dirichlet problem driven by a(p,q)-Laplace differential operator(1<q<p).The reaction is(p-1)-linear near±∞and the problem is noncoercive.Using variational tools and truncation and c...We consider a nonlinear Dirichlet problem driven by a(p,q)-Laplace differential operator(1<q<p).The reaction is(p-1)-linear near±∞and the problem is noncoercive.Using variational tools and truncation and comparison techniques together with critical groups,we produce five nontrivial smooth solutions all with sign information and ordered.In the particular case when q=2,we produce a second nodal solution for a total of six nontrivial smooth solutions all with sign information.展开更多
We consider a nonlinear Robin problem driven by the(p,q)-Laplacian plus an indefinite potential term and with a parametric reaction term.Under minimal conditions on the reaction function,which concern only its behavio...We consider a nonlinear Robin problem driven by the(p,q)-Laplacian plus an indefinite potential term and with a parametric reaction term.Under minimal conditions on the reaction function,which concern only its behavior near zero,we show that,for all λ>0 small,the problem has a nodal solution y_(λ)∈C^(1)(Ω)and we have y_(λ)→0 in C^(1)(Ω)asλ→0^(+).展开更多
Owing to the large amplitude and nonlinearity of extreme sea waves,sailing ships exhibit obvious large-amplitude motion and green water.For a tumblehome vessel,a low-tumblehome freeboard and wave-piercing bow make gre...Owing to the large amplitude and nonlinearity of extreme sea waves,sailing ships exhibit obvious large-amplitude motion and green water.For a tumblehome vessel,a low-tumblehome freeboard and wave-piercing bow make green water more likely.To study the green water of a wave-facing sailing tumblehome vessel in strong nonlinear regular waves,the computational fluid dynamics software STAR-CCM+was used.The Reynolds-averaged Navier–Stokes method was used for the numerical simulation,and the k-epsilon model was adopted to deal with viscous turbulence.The volume of the fluid method was used to capture the free surface,and overset grids were utilized to simulate the large-amplitude ship motion.This study delves into the influence of wave height on the ship motion response and a tumblehome vessel green water under a large wave steepness(0.033≤H/λ≤0.067)at Fr=0.22.In addition,the dynamic process of green water and the“wave run-up”phenomenon were evaluated.The results suggest that when the wavelength is equal to the ship length and the wave steepness increases to 0.056,the increase in the water height on the deck is obvious.However,the wave height had little effect on the green water duration.The wave steepness and“backwater”have a great impact on the value and number of the peak of the water height on the deck.When the wave steepness exceeded 0.056,the water climbed up,and the plunging-type water body was formed at the top of the wave baffle,resulting in a large water area on the deck.展开更多
The aim of this paper is to study the long-term behavior of strongly damped wave equations with a Lyapunov function. Using the theory established by estimating the Z2 index of some sets and the idea of invariant sets ...The aim of this paper is to study the long-term behavior of strongly damped wave equations with a Lyapunov function. Using the theory established by estimating the Z2 index of some sets and the idea of invariant sets of semi-flow,the properties of the global attractor for strongly damped wave equation are discussed. The existence of multiple equilibrium points in global attractor for strongly damped wave equations with critical growth of nonlinearity is obtained. And under some additional condition, the infinite dimension of the attractor is proven.展开更多
The global boundness and existence are presented for the kind of the Rosseland equation with a general growth condition. A linearized map in a closed convex set is defined. The image set is precompact, and thus a fixe...The global boundness and existence are presented for the kind of the Rosseland equation with a general growth condition. A linearized map in a closed convex set is defined. The image set is precompact, and thus a fixed point exists. A multi-scale expansion method is used to obtain the homogenized equation. This equation satisfies a similar growth condition.展开更多
We consider a Dirichlet nonlinear equation driven by the(p,2)-Laplacian and with a reaction having the competing effects of a parametric asymmetric superlinear term and a resonant perturbation.We show that for all sma...We consider a Dirichlet nonlinear equation driven by the(p,2)-Laplacian and with a reaction having the competing effects of a parametric asymmetric superlinear term and a resonant perturbation.We show that for all small values of the parameter the problem has at least five nontrivial smooth solutions all with sign information.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
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11504027 and 11847011)
文摘We propose a regular spherically symmetric spacetime solution with three parameters in Einstein gravity coupled to nonlinear electrodynamics(NED), which describes the NED black hole with electric charge. It is found that the system enclosed by the horizon of NED spacetime satisfies the first law of thermodynamics. In order to obtain the NED spacetime with only electric charge, the case of two parameters taking the same value is considered. In this case, we express the mass of the NED spacetime as a function of the entropy and electric charge of the NED black hole, give the Smarr-like formula and the approximate Smarr formula for the mass of NED spacetime.
基金supported by the National Science Fund for Distinguished Young Scholars(11125209)the National Natural Science Foundation of China(51121063 and 10702039)
文摘This paper is concerned with the connection between the Volterra series and the regular perturbation method in nonlinear systems analyses. It is revealed for the first time that, for a forced polynomial nonlinear system, if its derived linear system is a damped dissipative system, the steady response obtained through the regular perturbation method is exactly identical to the response given by the Volterra series. On the other hand, if the derived linear system is an undamped conservative system, then the Volterra series is incapable of modeling the forced polynomial nonlinear system. Numerical examples are further presented to illustrate these points. The results provide a new criterion for quickly judging whether the Volterra series is applicable for modeling a given polynomial nonlinear system.
基金supported by the Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme under Grant Agreement No.295118the National Science Center of Poland under grant No.N N201 604640+1 种基金the International Project co-financed by the Ministry of Science and Higher Education of Republic of Poland under grant No.W111/7.PR/2012the National Science Center of Poland under Maestro Advanced Project No.DEC2012/06/A/ST1/00262
文摘We consider a parametric Dirichlet problem driven by the p-Laplacian with a Caratheodory reaction of equidiffusive type. Our hypotheses incorporate as a special case the equidiffusive p-logistic equation. We show that if λ1 〉 0 is the principal eigenvalue of the Dirichlet negative p-Laplacian and ）λ 〉 λ1 （/k being the parameter）, the problem has a unique positive solution, while for ）λ ∈ （0, λ1], the problem has no positive solution.
文摘We consider a nonlinear Dirichlet problem driven by a(p,q)-Laplace differential operator(1<q<p).The reaction is(p-1)-linear near±∞and the problem is noncoercive.Using variational tools and truncation and comparison techniques together with critical groups,we produce five nontrivial smooth solutions all with sign information and ordered.In the particular case when q=2,we produce a second nodal solution for a total of six nontrivial smooth solutions all with sign information.
基金supported by Piano della Ricerca di Ateneo 2020-2022-PIACERIProject MO.S.A.I.C"Monitoraggio satellitare,modellazioni matematiche e soluzioni architettoniche e urbane per lo studio,la previsione e la mitigazione delle isole di calore urbano",Project EEEP&DLaD.S。
文摘We consider a nonlinear Robin problem driven by the(p,q)-Laplacian plus an indefinite potential term and with a parametric reaction term.Under minimal conditions on the reaction function,which concern only its behavior near zero,we show that,for all λ>0 small,the problem has a nodal solution y_(λ)∈C^(1)(Ω)and we have y_(λ)→0 in C^(1)(Ω)asλ→0^(+).
基金Supported by the Heilongjiang Touyan Project of Chinaand the Frontier Science Center of the Ministry of Education for Extreme Marine Environment Wave Fields
文摘Owing to the large amplitude and nonlinearity of extreme sea waves,sailing ships exhibit obvious large-amplitude motion and green water.For a tumblehome vessel,a low-tumblehome freeboard and wave-piercing bow make green water more likely.To study the green water of a wave-facing sailing tumblehome vessel in strong nonlinear regular waves,the computational fluid dynamics software STAR-CCM+was used.The Reynolds-averaged Navier–Stokes method was used for the numerical simulation,and the k-epsilon model was adopted to deal with viscous turbulence.The volume of the fluid method was used to capture the free surface,and overset grids were utilized to simulate the large-amplitude ship motion.This study delves into the influence of wave height on the ship motion response and a tumblehome vessel green water under a large wave steepness(0.033≤H/λ≤0.067)at Fr=0.22.In addition,the dynamic process of green water and the“wave run-up”phenomenon were evaluated.The results suggest that when the wavelength is equal to the ship length and the wave steepness increases to 0.056,the increase in the water height on the deck is obvious.However,the wave height had little effect on the green water duration.The wave steepness and“backwater”have a great impact on the value and number of the peak of the water height on the deck.When the wave steepness exceeded 0.056,the water climbed up,and the plunging-type water body was formed at the top of the wave baffle,resulting in a large water area on the deck.
基金National Natural Science Foundations of China(Nos.11501096,11526100)Fundamental Research Funds for the Central Universities,China(No.2232015D3-36)+1 种基金Natural Science Fund for Colleges and Universities in Jiangsu Province,China(No.15KJB110005)Qinglan Project,China
文摘The aim of this paper is to study the long-term behavior of strongly damped wave equations with a Lyapunov function. Using the theory established by estimating the Z2 index of some sets and the idea of invariant sets of semi-flow,the properties of the global attractor for strongly damped wave equation are discussed. The existence of multiple equilibrium points in global attractor for strongly damped wave equations with critical growth of nonlinearity is obtained. And under some additional condition, the infinite dimension of the attractor is proven.
基金Supported by the National Basic Research Program of China(973 Program)(No.2012CB025904)the National Natural Science Foundation of China(No.90916027)
文摘The global boundness and existence are presented for the kind of the Rosseland equation with a general growth condition. A linearized map in a closed convex set is defined. The image set is precompact, and thus a fixed point exists. A multi-scale expansion method is used to obtain the homogenized equation. This equation satisfies a similar growth condition.
基金NNSF of China(Grant No.12071413)NSF of Guangxi(Grant No.2023GXNSFAA026085)the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement No.823731 CONMECH。
文摘We consider a Dirichlet nonlinear equation driven by the(p,2)-Laplacian and with a reaction having the competing effects of a parametric asymmetric superlinear term and a resonant perturbation.We show that for all small values of the parameter the problem has at least five nontrivial smooth solutions all with sign information.
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.
