Homoclinic solutions were introduced for a prescribed mean curvature Lienard p-Laplacian equation with a deviating argument.It was divided into three parts to discuss the existence of homoclinic solutions.By using an ...Homoclinic solutions were introduced for a prescribed mean curvature Lienard p-Laplacian equation with a deviating argument.It was divided into three parts to discuss the existence of homoclinic solutions.By using an extension of Mawhin's continuation theorem,the existence of a set with 2kT-periodic for a prescribed mean curvature Lienard p-Laplacian equation with a deviating argument was studied.According to a limit on a certain subsequence of 2kT-periodic set,homoclinic solutions were obtained.A numerical example demonstrates the validity of the main results.展开更多
This paper deals with the following prescribed boundary mean curvature problem in B^(N){−Δu=0,u>0,∂_(u)∂_(ν)+N−2/2 u=N−2/2 K˜(y)u^(2−1),y∈B^(N)y∈S^(N−1),where K˜(y)=K˜(|y|,y˜)is a bounded nonnegative function w...This paper deals with the following prescribed boundary mean curvature problem in B^(N){−Δu=0,u>0,∂_(u)∂_(ν)+N−2/2 u=N−2/2 K˜(y)u^(2−1),y∈B^(N)y∈S^(N−1),where K˜(y)=K˜(|y|,y˜)is a bounded nonnegative function with y=(y,y˜)∈R^(2)×R^(N−3),2=2(N−1)/N−2.Combining the finite-dimensional reduction method and local Pohozaev type of identities,we prove that if N≥5 and K˜(r,y˜)has a stable critical point(r_(0),y˜_(0))with r0>0 and K˜(r0,y˜0)>0,then the above problem has infinitely many solutions,whose energy can be made arbitrarily large.Here our result fill the gap that the above critical points may include the saddle points of K˜(r,y˜).展开更多
We study the existence of multiple positive solutions for a Neumann problem with singular φ-Laplacian{-(φ（u′）)′= λf（u）, x ∈（0, 1）,u′（0） = 0 = u′（1）,where λ is a positive parameter, φ（s） =s/（1-s;...We study the existence of multiple positive solutions for a Neumann problem with singular φ-Laplacian{-(φ（u′）)′= λf（u）, x ∈（0, 1）,u′（0） = 0 = u′（1）,where λ is a positive parameter, φ（s） =s/（1-s;）;, f ∈ C;（[0, ∞）, R), f′（u） > 0 for u > 0, and for some 0 < β < θ such that f（u） < 0 for u ∈ [0, β)（semipositone） and f（u） > 0 for u > β.Under some suitable assumptions, we obtain the existence of multiple positive solutions of the above problem by using the quadrature technique. Further, if f ∈ C;（[0, β） ∪（β, ∞）, R),f′′（u） ≥ 0 for u ∈ [0, β) and f′′（u） ≤ 0 for u ∈（β, ∞）, then there exist exactly 2 n + 1 positive solutions for some interval of λ, which is dependent on n and θ. Moreover, We also give some examples to apply our results.展开更多
基金Natural Foundation of Wuyi University,China(No.XQ201305)Young-Middle-Aged Teachers Education Scientific Research Project in Fujian Province,China(No.JA15524)
文摘Homoclinic solutions were introduced for a prescribed mean curvature Lienard p-Laplacian equation with a deviating argument.It was divided into three parts to discuss the existence of homoclinic solutions.By using an extension of Mawhin's continuation theorem,the existence of a set with 2kT-periodic for a prescribed mean curvature Lienard p-Laplacian equation with a deviating argument was studied.According to a limit on a certain subsequence of 2kT-periodic set,homoclinic solutions were obtained.A numerical example demonstrates the validity of the main results.
基金Supported by NSFC(Grant Nos.12226324,11961043,11801226)。
文摘This paper deals with the following prescribed boundary mean curvature problem in B^(N){−Δu=0,u>0,∂_(u)∂_(ν)+N−2/2 u=N−2/2 K˜(y)u^(2−1),y∈B^(N)y∈S^(N−1),where K˜(y)=K˜(|y|,y˜)is a bounded nonnegative function with y=(y,y˜)∈R^(2)×R^(N−3),2=2(N−1)/N−2.Combining the finite-dimensional reduction method and local Pohozaev type of identities,we prove that if N≥5 and K˜(r,y˜)has a stable critical point(r_(0),y˜_(0))with r0>0 and K˜(r0,y˜0)>0,then the above problem has infinitely many solutions,whose energy can be made arbitrarily large.Here our result fill the gap that the above critical points may include the saddle points of K˜(r,y˜).
文摘We study the existence of multiple positive solutions for a Neumann problem with singular φ-Laplacian{-(φ（u′）)′= λf（u）, x ∈（0, 1）,u′（0） = 0 = u′（1）,where λ is a positive parameter, φ（s） =s/（1-s;）;, f ∈ C;（[0, ∞）, R), f′（u） > 0 for u > 0, and for some 0 < β < θ such that f（u） < 0 for u ∈ [0, β)（semipositone） and f（u） > 0 for u > β.Under some suitable assumptions, we obtain the existence of multiple positive solutions of the above problem by using the quadrature technique. Further, if f ∈ C;（[0, β） ∪（β, ∞）, R),f′′（u） ≥ 0 for u ∈ [0, β) and f′′（u） ≤ 0 for u ∈（β, ∞）, then there exist exactly 2 n + 1 positive solutions for some interval of λ, which is dependent on n and θ. Moreover, We also give some examples to apply our results.
