We consider the following eigenvalue problem: [GRAPHICS] Where f(x, t) is a continuous function with critical growth. We prove the existence of nontrivial solutions.
In this paper, it is proved that the following boundary value problem [GRAPHICS] admits infinitely many solution for 0 < lambda < lambda-1, n greater-than-or-equal-to 5 and for ball regions OMEGA = B(R)(0).
In this paper,we study the following critical elliptic problem with a variable exponent:{-Δu=u^(p+ϵa(x))inΩ,u>0 inΩ,u=0 on∂Ω,where a(x)2∈C^(2)(Ω),p=N+2/N-2,∈>0,andΩis a smooth bounded domain in R^(N)(N&g...In this paper,we study the following critical elliptic problem with a variable exponent:{-Δu=u^(p+ϵa(x))inΩ,u>0 inΩ,u=0 on∂Ω,where a(x)2∈C^(2)(Ω),p=N+2/N-2,∈>0,andΩis a smooth bounded domain in R^(N)(N>4).We show that for∈small enough,there exists a family of bubble solutions concentrating at the negative stable critical point of the function a(x).This is a new perturbation to the critical elliptic equation in contrast to the usual subcritical or supercritical perturbation,and gives the first existence result for the critical elliptic problem with a variable exponent.展开更多
In this paper, we get the existence of a weak solution of the following inhomogeneous quasilinear elliptic equation with critical growth conditions: where N≥2, f(x,u)~|u|<sup>m-1</sup>e<sup>b|u|&...In this paper, we get the existence of a weak solution of the following inhomogeneous quasilinear elliptic equation with critical growth conditions: where N≥2, f(x,u)~|u|<sup>m-1</sup>e<sup>b|u|<sup>γ</sup></sup>at +∞, with γ=N/N-1, m≥1, b】0.展开更多
文摘We consider the following eigenvalue problem: [GRAPHICS] Where f(x, t) is a continuous function with critical growth. We prove the existence of nontrivial solutions.
文摘In this paper, it is proved that the following boundary value problem [GRAPHICS] admits infinitely many solution for 0 < lambda < lambda-1, n greater-than-or-equal-to 5 and for ball regions OMEGA = B(R)(0).
基金supported by National Natural Science Foundation of China(Grant No.11971147)supported by National Natural Science Foundation of China(Grant Nos.11831009 and 12171183)the Fundamental Research Funds for the Central Universities(Grant No.KJ02072020-0319).
文摘In this paper,we study the following critical elliptic problem with a variable exponent:{-Δu=u^(p+ϵa(x))inΩ,u>0 inΩ,u=0 on∂Ω,where a(x)2∈C^(2)(Ω),p=N+2/N-2,∈>0,andΩis a smooth bounded domain in R^(N)(N>4).We show that for∈small enough,there exists a family of bubble solutions concentrating at the negative stable critical point of the function a(x).This is a new perturbation to the critical elliptic equation in contrast to the usual subcritical or supercritical perturbation,and gives the first existence result for the critical elliptic problem with a variable exponent.
基金Supported by the Youth FoundationNatural Science Foundation, People's Republic of China.
文摘In this paper, we get the existence of a weak solution of the following inhomogeneous quasilinear elliptic equation with critical growth conditions: where N≥2, f(x,u)~|u|<sup>m-1</sup>e<sup>b|u|<sup>γ</sup></sup>at +∞, with γ=N/N-1, m≥1, b】0.