In this paper, using the decay estimates for the solution of semilinear elliptic equation, we obtain the existence of a minimun for a minimization problem with nonzero data in the exterior domain.
In this paper we deal with the existence of infinitely many critical points of the even functional I（u）=integral from n=Q to （F（x,u,Du））+integral from n=（?）Q to （G（x,u））, u∈W<sup>1,p</sup>（Ω...In this paper we deal with the existence of infinitely many critical points of the even functional I（u）=integral from n=Q to （F（x,u,Du））+integral from n=（?）Q to （G（x,u））, u∈W<sup>1,p</sup>（Ω）,where G（x, u）=integral from n=o to u （g（x,t）dt）, under the weak structure conditions on F（x, u, q） by the Mountain Pass Lemma.展开更多
In this paper, we study the following eigenvalue problem involving limiting nonlinearity by a new way of using the concentration-compactness principle. Even in the nonlimiting situation, we improve the known result in...In this paper, we study the following eigenvalue problem involving limiting nonlinearity by a new way of using the concentration-compactness principle. Even in the nonlimiting situation, we improve the known result in the positive mass case in the sense of seeking a nontrivial solution of the above eigenvalue problem.展开更多
We use the blow-up method to get the C<sup>1,α</sup> partial regularity results for the following elliptic systems satisfying natural growth conditions:
In this paper, we establish fountain theorems over cones and apply it to the quasilinear elliptic problem{-pu = λ|u|q-2u + μ|u| γ-2 u, x ∈Ω,u = 0, x ∈Ω,(1)to show that problem (1) possesses infinitely many so...In this paper, we establish fountain theorems over cones and apply it to the quasilinear elliptic problem{-pu = λ|u|q-2u + μ|u| γ-2 u, x ∈Ω,u = 0, x ∈Ω,(1)to show that problem (1) possesses infinitely many solutions, where 1 < p < N, 1 < q < p < γ, ΩRN is a smooth bounded domain and λ, μ∈ R.展开更多
We study the following elliptic problem:{-div(a(x)Du)=Q(x)|u|2-2u+λu x ∈Ω ,u=0 on ΩUnder certain assumptions on a and Q, we obtain existence of infinitely many solutions by variational method.
In this paper, we continue to construct stationary classical solutions for the incompressible planar flows approximating singular stationary solutions of this problem. This procedure is carried out by constructing sol...In this paper, we continue to construct stationary classical solutions for the incompressible planar flows approximating singular stationary solutions of this problem. This procedure is carried out by constructing solutions for the following elliptic equations {-?u = λ∑kj=1 B_(δ(x_0,j))(u-κ_j)p+, in ?,u = 0, on ??,where 0 < p < 1, ? R^2 is a bounded simply-connected smooth domain, κi(i = 1, …, k) is prescribed positive constant. The result we prove is that for any given non-degenerate critical point x0 =(x0,1, …, x0,k) of the Kirchhoff-Routh function defined on ?kcorresponding to(κ1, …, κk), there exists a stationary classical solution approximating stationary k points vortex solution. Moreover, as λ→ +∞, the vorticity setcal vorticity strength near each x0,j appr y : uλ > κjoaches κj, j = ∩ Bδ(x0,j) shrinks to{x0,j}, and the lo 1, …, k. This result makes the study of the above problem with p ≥ 0 complete since the cases p > 1, p = 1, p = 0 have already been studied in [11, 12] and [13] respectively.展开更多
基金This work is supported by Youth Foundation, NSFC.
文摘In this paper, using the decay estimates for the solution of semilinear elliptic equation, we obtain the existence of a minimun for a minimization problem with nonzero data in the exterior domain.
文摘In this paper we deal with the existence of infinitely many critical points of the even functional I（u）=integral from n=Q to （F（x,u,Du））+integral from n=（?）Q to （G（x,u））, u∈W<sup>1,p</sup>（Ω）,where G（x, u）=integral from n=o to u （g（x,t）dt）, under the weak structure conditions on F（x, u, q） by the Mountain Pass Lemma.
基金This work is supported by the Youth Foundation, NSFC.
文摘In this paper, we get the existence result of the nontrivial weak solution (λ, u) of the following eigenvalue problem with natural growth conditions.
文摘In this paper, we study the following eigenvalue problem involving limiting nonlinearity by a new way of using the concentration-compactness principle. Even in the nonlimiting situation, we improve the known result in the positive mass case in the sense of seeking a nontrivial solution of the above eigenvalue problem.
文摘We use the blow-up method to get the C<sup>1,α</sup> partial regularity results for the following elliptic systems satisfying natural growth conditions:
基金supported by ARC grant of Australiasupported by National Natural Sciences Foundations of China (10961016 and 10631030)NSF of Jiangxi(2009GZS0011)
文摘In this paper, we establish fountain theorems over cones and apply it to the quasilinear elliptic problem{-pu = λ|u|q-2u + μ|u| γ-2 u, x ∈Ω,u = 0, x ∈Ω,(1)to show that problem (1) possesses infinitely many solutions, where 1 < p < N, 1 < q < p < γ, ΩRN is a smooth bounded domain and λ, μ∈ R.
基金supported by Key Project (10631030) of NSFCKnowledge Innovation Funds of CAS in Chinasupported by ARC in Australia
文摘We study the following elliptic problem:{-div(a(x)Du)=Q(x)|u|2-2u+λu x ∈Ω ,u=0 on ΩUnder certain assumptions on a and Q, we obtain existence of infinitely many solutions by variational method.
文摘In this paper, we continue to construct stationary classical solutions for the incompressible planar flows approximating singular stationary solutions of this problem. This procedure is carried out by constructing solutions for the following elliptic equations {-?u = λ∑kj=1 B_(δ(x_0,j))(u-κ_j)p+, in ?,u = 0, on ??,where 0 < p < 1, ? R^2 is a bounded simply-connected smooth domain, κi(i = 1, …, k) is prescribed positive constant. The result we prove is that for any given non-degenerate critical point x0 =(x0,1, …, x0,k) of the Kirchhoff-Routh function defined on ?kcorresponding to(κ1, …, κk), there exists a stationary classical solution approximating stationary k points vortex solution. Moreover, as λ→ +∞, the vorticity setcal vorticity strength near each x0,j appr y : uλ > κjoaches κj, j = ∩ Bδ(x0,j) shrinks to{x0,j}, and the lo 1, …, k. This result makes the study of the above problem with p ≥ 0 complete since the cases p > 1, p = 1, p = 0 have already been studied in [11, 12] and [13] respectively.
