We use the Morawetz multiplier to show that there are no nontrivial solutions of certain decay order for a biharmonic equation with a p-Laplacian term and a system of coupled biharmonic equations with p-Laplacian term...We use the Morawetz multiplier to show that there are no nontrivial solutions of certain decay order for a biharmonic equation with a p-Laplacian term and a system of coupled biharmonic equations with p-Laplacian terms in the entire Euclidean space.展开更多
Based on the endpoint Strichartz estimates for the fourth order SchrSdinger equation with potentials for n ≥ 5 by [Feng, H., Softer, A., Yao, X.： Decay estimates and Strichartz estimates of the fourth-order Schr6din...Based on the endpoint Strichartz estimates for the fourth order SchrSdinger equation with potentials for n ≥ 5 by [Feng, H., Softer, A., Yao, X.： Decay estimates and Strichartz estimates of the fourth-order Schr6dinger operator. J. Funct. Anal., 274, 605-658 （2018）], in this paper, the authors further derive Strichartz type estimates with gain of derivatives similar to the one in [Pausader, B.： The cubic fourth-order Schr6dinger equation. J. Funct. Anal., 256, 2473-2517 （2009）]. As their applications, we combine the classical Morawetz estimate and the interaction Morawetz estimate to establish scattering theory in the energy space for the defocusing fourth order NLS with potentials and pure power nonlinearity 1 ＋ 8/n〈 p 〈 1 ＋ 8/n-4 in dimensions n ≥ 7. n展开更多
The primary goal of this paper is to present a comprehensive study of the nonlinear Schrodinger equations with combined nonlinearities of the power-type and Hartreetype. Under certain structural conditions, the author...The primary goal of this paper is to present a comprehensive study of the nonlinear Schrodinger equations with combined nonlinearities of the power-type and Hartreetype. Under certain structural conditions, the authors are able to provide a complete picture of how the nonlinear Schrodinger equations with combined nonlinearities interact in the given energy space. The method used in the paper is based upon the Morawetz estimates and perturbation principles.展开更多
The purpose of this paper is to study scattering theory for the energy subcritical solutions to the non-radial defocusing inhomogeneous Hartree equation iδ_(t)u+Δu=(I_(a)*|·|^(b)|u|^(p))|·|^(b)|u|^(p-2)u.T...The purpose of this paper is to study scattering theory for the energy subcritical solutions to the non-radial defocusing inhomogeneous Hartree equation iδ_(t)u+Δu=(I_(a)*|·|^(b)|u|^(p))|·|^(b)|u|^(p-2)u.Taking advantage of the decay factor in the nonlinearity instead of the embedding theorem,we establish the scattering criterion for the equation.Together with the Morawetz estimate,we obtain the scattering theory for the energy-subcritical case.展开更多
In this paper,we consider the defocusing nonlinear Schrodinger equation in space dimensions d≥4.We prove that if u is a radial solution which is priori bounded inthe critical Sobolev space,that is,u L∈L_(t)^(∞)H_(x...In this paper,we consider the defocusing nonlinear Schrodinger equation in space dimensions d≥4.We prove that if u is a radial solution which is priori bounded inthe critical Sobolev space,that is,u L∈L_(t)^(∞)H_(x)^(Sc),then u is global and scatters.In practise,we use weighted Strichartz space adapted for our setting which ultimately helps us solve the problems in cases d≥4 and 0<sc<1/2 The results in this paper extend the work of[27,Commun.PDEs,40(2015),265-308]to higher dimensions.展开更多
文摘We use the Morawetz multiplier to show that there are no nontrivial solutions of certain decay order for a biharmonic equation with a p-Laplacian term and a system of coupled biharmonic equations with p-Laplacian terms in the entire Euclidean space.
基金supported by the China National Science Foundation(Grant Nos.11371158 and 11771165)the second author is supported by the China National Science Foundation(Grant Nos.11101172 and 11571131)
文摘Based on the endpoint Strichartz estimates for the fourth order SchrSdinger equation with potentials for n ≥ 5 by [Feng, H., Softer, A., Yao, X.： Decay estimates and Strichartz estimates of the fourth-order Schr6dinger operator. J. Funct. Anal., 274, 605-658 （2018）], in this paper, the authors further derive Strichartz type estimates with gain of derivatives similar to the one in [Pausader, B.： The cubic fourth-order Schr6dinger equation. J. Funct. Anal., 256, 2473-2517 （2009）]. As their applications, we combine the classical Morawetz estimate and the interaction Morawetz estimate to establish scattering theory in the energy space for the defocusing fourth order NLS with potentials and pure power nonlinearity 1 ＋ 8/n〈 p 〈 1 ＋ 8/n-4 in dimensions n ≥ 7. n
基金Project supported by the National Natural Science Foundation of China(Nos.10871175,10931007)the Zhejiang Provincial Natural Science Foundation of China(No.Z6100217)
文摘The primary goal of this paper is to present a comprehensive study of the nonlinear Schrodinger equations with combined nonlinearities of the power-type and Hartreetype. Under certain structural conditions, the authors are able to provide a complete picture of how the nonlinear Schrodinger equations with combined nonlinearities interact in the given energy space. The method used in the paper is based upon the Morawetz estimates and perturbation principles.
基金supported by Qinghai Natural Science Foundation(No.2024-ZJ-976).
文摘The purpose of this paper is to study scattering theory for the energy subcritical solutions to the non-radial defocusing inhomogeneous Hartree equation iδ_(t)u+Δu=(I_(a)*|·|^(b)|u|^(p))|·|^(b)|u|^(p-2)u.Taking advantage of the decay factor in the nonlinearity instead of the embedding theorem,we establish the scattering criterion for the equation.Together with the Morawetz estimate,we obtain the scattering theory for the energy-subcritical case.
基金supported in part by the National Natural Science Foundation of China under grant No.11671047 and No.11726005supported by the LabEx MME-DII
文摘In this paper,we consider the defocusing nonlinear Schrodinger equation in space dimensions d≥4.We prove that if u is a radial solution which is priori bounded inthe critical Sobolev space,that is,u L∈L_(t)^(∞)H_(x)^(Sc),then u is global and scatters.In practise,we use weighted Strichartz space adapted for our setting which ultimately helps us solve the problems in cases d≥4 and 0<sc<1/2 The results in this paper extend the work of[27,Commun.PDEs,40(2015),265-308]to higher dimensions.
