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MULTIPLE POSITIVE SOLUTIONS FOR QUASILINEAR ELLIPTIC PROBLEMS INVOLVING CONCAVE-CONVEX NONLINEARITIES AND MULTIPLE HARDY-TYPE TERMS 被引量:3
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作者 Tsing-San HSU 《Acta Mathematica Scientia》 SCIE CSCD 2013年第5期1314-1328,共15页
In this paper, we deal with the existence and multiplicity of positive solutions for the quasilinear elliptic problem -△pu-∑i=1^kμi|u|^p-2/|x-ai|p^u=|u|^p^*-2u+λ|u|^q-2u,x∈Ω,where Ω belong to R^N(N ... In this paper, we deal with the existence and multiplicity of positive solutions for the quasilinear elliptic problem -△pu-∑i=1^kμi|u|^p-2/|x-ai|p^u=|u|^p^*-2u+λ|u|^q-2u,x∈Ω,where Ω belong to R^N(N ≥ 3) is a smooth bounded domain such that the different points ai∈Ω,i= 1,2,...,k,0≤μi〈μ^-=(N-p/p)^p,λ〉0,1≤q〈p,and p^*=p^N/N-p.The results depend crucially cn the parameters λ,q and μi for i=1,2,...,k. 展开更多
关键词 multiple positive solutions concave-convex nonlinearities multiple Hardy- type terms
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Blow-Up Result for a Semi-Linear Wave Equation with a Nonlinear Memory Term of Derivative Type 被引量:1
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作者 OUYANG Bai-ping XIAO Sheng-zhong 《Chinese Quarterly Journal of Mathematics》 2021年第3期235-243,共9页
In this paper,we study the blow-up of solutions to a semi-linear wave equation with a nonlinear memory term of derivative type.By using methods of an iteration argument and di erential inequalities,we obtain the blow-... In this paper,we study the blow-up of solutions to a semi-linear wave equation with a nonlinear memory term of derivative type.By using methods of an iteration argument and di erential inequalities,we obtain the blow-up result for the semi-linear wave equation when the exponent of p is under certain conditions.Meanwhile,we derive an upper bound of the lifespan of solutions to the Cauchy problem for the semi-linear wave equation. 展开更多
关键词 Semi-linear wave equation BLOW-UP Nonlinear memory term of derivative type Lifespan
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Multiplicity of nontrivial solutions for Kirchhoff type equations with zero mass and a critical term 被引量:1
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作者 Chongqing WEI Anran LI 《Frontiers of Mathematics in China》 SCIE CSCD 2022年第5期813-828,共16页
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
关键词 Kirchhoff type equations with a critical term variational methods Symmetric Mountain Pass theorem Second Concentration Compactness lemma
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Qualitative Analysis of Van der Pol Type Equation with Periodic Forcing Term
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作者 郑志明 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1990年第3期243-256,共14页
In this paper we analyze the qualitative behaviour of the equation ε+q(X) +εX=bp(t), where e is a small parameter.We divide the interval of parameter b into four sets of subintervals,A, B,C and D.For bA,B or D,we di... In this paper we analyze the qualitative behaviour of the equation ε+q(X) +εX=bp(t), where e is a small parameter.We divide the interval of parameter b into four sets of subintervals,A, B,C and D.For bA,B or D,we discuss the different structures of the attractors of the equation and their stabilities.When chaotic phenomena appear,we also estimate the entropy.For bC,the set of bifurcation intervals,we analyze the bifurcating type and get a series of consequences from the results of Newhouse and Palis. 展开更多
关键词 PR Qualitative Analysis of Van der Pol Type Equation with Periodic Forcing term der
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