The multiplicity of periodic solutions for a class of second order Hamiltonian system with superquadratic plus subquadratic nonlinearity is studied in this paper.Obtained via the Symmetric Mountain Pass Lemma,two resu...The multiplicity of periodic solutions for a class of second order Hamiltonian system with superquadratic plus subquadratic nonlinearity is studied in this paper.Obtained via the Symmetric Mountain Pass Lemma,two results about infinitely many periodic solutions of the systems extend some previously known results.展开更多
In this paper we first improve the concentration- compactness lemma by proving that the vanishing case is a special case of dichotomy, then we apply this improved concentration- compactness lemma to a typical restrct...In this paper we first improve the concentration- compactness lemma by proving that the vanishing case is a special case of dichotomy, then we apply this improved concentration- compactness lemma to a typical restrcted minimization problem, and get some new results.展开更多
In this paper,the multiplicity of homoclinic solutions for second order non-autonomous Hamiltonian systemsü(t)-L(t)u(t)+▽uW(t,u(t))=0 is obtained via a new Symmetric Mountain Pass Lemma established by Kajikiya,w...In this paper,the multiplicity of homoclinic solutions for second order non-autonomous Hamiltonian systemsü(t)-L(t)u(t)+▽uW(t,u(t))=0 is obtained via a new Symmetric Mountain Pass Lemma established by Kajikiya,where L∈C(R,RN×N)is symmetric but non-periodic,W∈C1(R×RN,R)is locally even in u and only satisfies some growth conditions near u=0,which improves some previous results.展开更多
In this paper,a class of Kirchhoff type equations in R^(N)(N≥3)with zero mass and a critical term is studied.Under some appropriate conditions,the existence of multiple solutions is obtained by using variational meth...In this paper,a class of Kirchhoff type equations in R^(N)(N≥3)with zero mass and a critical term is studied.Under some appropriate conditions,the existence of multiple solutions is obtained by using variational methods and a variant of Symmetric Mountain Pass theorem.The Second Concentration Compactness lemma is used to overcome the lack of compactness in critical problem.Compared to the usual Kirchhoff-type problems,we only require the nonlinearity to satisfy the classical superquadratic condition(Ambrosetti-Rabinowitz condition).展开更多
In this paper,we present the singular supercritical Trudinger-Moser inequalities on the unit ball B in Rn,where n≥2.More precisely,we show that for any given α>0 and 0<t<n,then the following two inequalitie...In this paper,we present the singular supercritical Trudinger-Moser inequalities on the unit ball B in Rn,where n≥2.More precisely,we show that for any given α>0 and 0<t<n,then the following two inequalities hold for ∀u∈W^1,n0,r(B),∫Bsup∣▽u∣^ndx≤1∫Bexp((αn,t+∣x∣^α∣)u∣^n/n-1)/∣x∣^tdx<∞ and ∫Bsup∣▽u∣^ndx≤1∫Bexp(αn,t+∣u∣^n/n-1+∣x∣^α)/∣x∣^tdx<∞.We also consider the problem of the sharpness of the constantαn,t.Furthermore,by employing the method of estimating the lower bound and using the concentration-compactness principle,we establish the existence of extremals.These results extend the known results when t=0 to the singular version for 0<t<n.展开更多
基金Supported by National Natural Science Foundation of China (11371276,10901118)Elite Scholar Program in Tianjin University,P.R.China
文摘The multiplicity of periodic solutions for a class of second order Hamiltonian system with superquadratic plus subquadratic nonlinearity is studied in this paper.Obtained via the Symmetric Mountain Pass Lemma,two results about infinitely many periodic solutions of the systems extend some previously known results.
基金Supported by the National Natural Science Foundation of China (No.19871030, 19771039) and Natural Science Foundation of Guangd
文摘In this paper we first improve the concentration- compactness lemma by proving that the vanishing case is a special case of dichotomy, then we apply this improved concentration- compactness lemma to a typical restrcted minimization problem, and get some new results.
基金National Natural Science Foundation of China(Grant No.10901118)Elite Scholar Program in Tianjin University,P.R.China。
文摘In this paper,the multiplicity of homoclinic solutions for second order non-autonomous Hamiltonian systemsü(t)-L(t)u(t)+▽uW(t,u(t))=0 is obtained via a new Symmetric Mountain Pass Lemma established by Kajikiya,where L∈C(R,RN×N)is symmetric but non-periodic,W∈C1(R×RN,R)is locally even in u and only satisfies some growth conditions near u=0,which improves some previous results.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11701346,11671239,11801338)the Natural Science Foundation of Shanxi Province(Grant No.201801D211001)+1 种基金the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(Grant No.2019L0024)the Research Project Supported by Shanxi Scholarship Council of China(Grant No.2020-005).
文摘In this paper,a class of Kirchhoff type equations in R^(N)(N≥3)with zero mass and a critical term is studied.Under some appropriate conditions,the existence of multiple solutions is obtained by using variational methods and a variant of Symmetric Mountain Pass theorem.The Second Concentration Compactness lemma is used to overcome the lack of compactness in critical problem.Compared to the usual Kirchhoff-type problems,we only require the nonlinearity to satisfy the classical superquadratic condition(Ambrosetti-Rabinowitz condition).
基金Supported by NSFC(Grant No.11901031)Beijing Institute of Technology Research Fund Program for Young Scholars(Grant No.3170012221903)。
文摘In this paper,we present the singular supercritical Trudinger-Moser inequalities on the unit ball B in Rn,where n≥2.More precisely,we show that for any given α>0 and 0<t<n,then the following two inequalities hold for ∀u∈W^1,n0,r(B),∫Bsup∣▽u∣^ndx≤1∫Bexp((αn,t+∣x∣^α∣)u∣^n/n-1)/∣x∣^tdx<∞ and ∫Bsup∣▽u∣^ndx≤1∫Bexp(αn,t+∣u∣^n/n-1+∣x∣^α)/∣x∣^tdx<∞.We also consider the problem of the sharpness of the constantαn,t.Furthermore,by employing the method of estimating the lower bound and using the concentration-compactness principle,we establish the existence of extremals.These results extend the known results when t=0 to the singular version for 0<t<n.
