The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and e...The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and existence of uniform attractor under some suitable assumptions on the nonlinear term g(u),the nonlinear damping f(u_(t))and the external force h(x,t).Specifically,the asymptotic compactness of the semigroup is verified by the energy reconstruction method.展开更多
该文主要考虑一类在R^(3)上带有Kirchhoff型非局部项的非线性椭圆方程−(a+b∫_(R)^(3)|∇u|^(2))Δu+V(x)u=Q(x)|u|^(p−1)u,x∈R^(3),(0.1)其中a,b>0是常数,p∈(1,5),V(x)和Q(x)均为L^(∞)(R^(3))函数.由于非局部项的出现,若按经典的...该文主要考虑一类在R^(3)上带有Kirchhoff型非局部项的非线性椭圆方程−(a+b∫_(R)^(3)|∇u|^(2))Δu+V(x)u=Q(x)|u|^(p−1)u,x∈R^(3),(0.1)其中a,b>0是常数,p∈(1,5),V(x)和Q(x)均为L^(∞)(R^(3))函数.由于非局部项的出现,若按经典的思路来应用山路引理得到这类方程的解(即山路解),必须要求3≤p<5.当p∈(1,3)时,应用山路引理的困难在于无法验证(PS)序列的有界性.为克服该困难,文献[Acta Math Sci,2025,45B(2):385-400]通过引入新的技巧证明了方程(0.1)在Q(x)≡1时对p∈(1,5)有山路解,并讨论了山路解与基态解的关系.该文拟在克服V(x)和Q(x)的相互影响下,将文献[Acta Math Sci,2025,45B(2):385-400]中的结果推广到Q(x)■1的一般情形.展开更多
This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of norm...This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.11961059,1210502)the University Innovation Project of Gansu Province(Grant No.2023B-062)the Gansu Province Basic Research Innovation Group Project(Grant No.23JRRA684).
文摘The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and existence of uniform attractor under some suitable assumptions on the nonlinear term g(u),the nonlinear damping f(u_(t))and the external force h(x,t).Specifically,the asymptotic compactness of the semigroup is verified by the energy reconstruction method.
文摘该文主要考虑一类在R^(3)上带有Kirchhoff型非局部项的非线性椭圆方程−(a+b∫_(R)^(3)|∇u|^(2))Δu+V(x)u=Q(x)|u|^(p−1)u,x∈R^(3),(0.1)其中a,b>0是常数,p∈(1,5),V(x)和Q(x)均为L^(∞)(R^(3))函数.由于非局部项的出现,若按经典的思路来应用山路引理得到这类方程的解(即山路解),必须要求3≤p<5.当p∈(1,3)时,应用山路引理的困难在于无法验证(PS)序列的有界性.为克服该困难,文献[Acta Math Sci,2025,45B(2):385-400]通过引入新的技巧证明了方程(0.1)在Q(x)≡1时对p∈(1,5)有山路解,并讨论了山路解与基态解的关系.该文拟在克服V(x)和Q(x)的相互影响下,将文献[Acta Math Sci,2025,45B(2):385-400]中的结果推广到Q(x)■1的一般情形.
基金Supported by National Natural Science Foundation of China(11671403,11671236)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature.
