In this paper, the existence and nonexistence of solutions to a class of quasilinear elliptic equations with nonsmooth functionals are discussed, and the results obtained are applied to quasilinear SchrSdinger equatio...In this paper, the existence and nonexistence of solutions to a class of quasilinear elliptic equations with nonsmooth functionals are discussed, and the results obtained are applied to quasilinear SchrSdinger equations with negative parameter which arose from the study of self-channeling of high-power ultrashort laser in matter.展开更多
This note is a continuation of the work[17].We study the following quasilinear elliptic equations- △pu-μ/｜x｜p ｜u｜p-2 u=Q（x）｜u｜Np/N-p -2u,x∈R N,where 1 〈 p 〈 N,0 ≤ μ 〈（（N-p）/p）p and Q ∈ L∞（RN）.O...This note is a continuation of the work[17].We study the following quasilinear elliptic equations- △pu-μ/｜x｜p ｜u｜p-2 u=Q（x）｜u｜Np/N-p -2u,x∈R N,where 1 〈 p 〈 N,0 ≤ μ 〈（（N-p）/p）p and Q ∈ L∞（RN）.Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity.展开更多
The existence and multiplicity of positive solutions are studied for a class of quasi- linear elliptic equations involving Sobolev critical exponents with mixed Dirichlet-Neumann boundary conditions by the variational...The existence and multiplicity of positive solutions are studied for a class of quasi- linear elliptic equations involving Sobolev critical exponents with mixed Dirichlet-Neumann boundary conditions by the variational methods and some analytical techniques.展开更多
In this paper, we establish the existence of three weak solutions for quasilinear elliptic equations in an Orlicz-Sobolev space via an abstract result recently obtained by Ricceri in [13].
The article proved the existence of H<sup>1</sup> （R） ∩ L<sup>∞</sup> （R<sup>n</sup>） at the bifurcation λ= 0 by discussing the following nonlinear eigenvalue:—D-（ij）(a<...The article proved the existence of H<sup>1</sup> （R） ∩ L<sup>∞</sup> （R<sup>n</sup>） at the bifurcation λ= 0 by discussing the following nonlinear eigenvalue:—D-（ij）(a<sub>ij</sub>（x,u）D<sub>j</sub>u) +1/2a<sub>iju</sub>（x,u）D<sub>i</sub>uD<sub>j</sub>u — q（x）|u|<sup>σ</sup>u = λu0≠u∈H<sup>1</sup>（R<sup>n</sup>） ,0【σ【 4/n,n≥3,x∈ R<sup>n</sup>Meanwhile the article studied the conditions of q（x） under which λ=0 was a bifurcation point for the nonlinear eigenvalue . Here a<sub>ij</sub> are not required to be bounded as u varies.展开更多
In this article, we consider existence and nonexistence of solutions to problem {-△pu＋g（x,u）｜↓△｜^p=f in -Ω,u=0 on Ω with 1〈p〈∞ where f is a positive measurable function which is bounded away from 0 in Ω,...In this article, we consider existence and nonexistence of solutions to problem {-△pu＋g（x,u）｜↓△｜^p=f in -Ω,u=0 on Ω with 1〈p〈∞ where f is a positive measurable function which is bounded away from 0 in Ω, and the domain Ω is a smooth bounded open set in R^N（N≥2）. Especially, under the condition that g（x, s） = 1/｜s｜^α （α〉0） is singular at s = 0, we obtain that α 〈 p is necessary and sufficient for the existence of solutions in W0^1,p（Ω） to problem （0.1） when f is sufficiently regular.展开更多
We prove the existence of a ground state solution for the qusilinear elliptic equation in , under suitable conditions on a locally Holder continuous non-linearity , the non-linearity may exhibit a singularity as . We ...We prove the existence of a ground state solution for the qusilinear elliptic equation in , under suitable conditions on a locally Holder continuous non-linearity , the non-linearity may exhibit a singularity as . We also prove the non-existence of radially symmetric solutions to the singular elliptic equation in , as where .展开更多
The existence ofpositive radialsolutions ofthe equation - div(｜Du｜p- 2Du)= f(u) is studied in annular dom ains in Rn,n≥2. Itisproved thatiff(0)≥0, f is somewhere negativein (0,∞), lim u→0+ f′(u)= 0and lim u→...The existence ofpositive radialsolutions ofthe equation - div(｜Du｜p- 2Du)= f(u) is studied in annular dom ains in Rn,n≥2. Itisproved thatiff(0)≥0, f is somewhere negativein (0,∞), lim u→0+ f′(u)= 0and lim u→∞(f(u)/up- 1)= ∞, then thereisa largepositiveradialsolution on allannuli.Iff(0)< 0 and satisfiescertain condi- tions, then the equation has no radialsolution ifthe annuliare too wide.展开更多
In this paper, the existence and nonexistence of nonnegative entire large solutions for the quasilinear elliptic equation are established, where , and are nondecreasing and vanish at the origin. The locally H lder con...In this paper, the existence and nonexistence of nonnegative entire large solutions for the quasilinear elliptic equation are established, where , and are nondecreasing and vanish at the origin. The locally H lder continuous functions and are nonnegative. We extend results previously obtained for special cases of and g.展开更多
基金supported by NSF of China(11201488),supported by NSF of China(11371146)Hunan Provincial Natural Science Foundation of China(14JJ4002)
文摘In this paper, the existence and nonexistence of solutions to a class of quasilinear elliptic equations with nonsmooth functionals are discussed, and the results obtained are applied to quasilinear SchrSdinger equations with negative parameter which arose from the study of self-channeling of high-power ultrashort laser in matter.
基金financially supported by the Academy of Finland,project 259224
文摘This note is a continuation of the work[17].We study the following quasilinear elliptic equations- △pu-μ/｜x｜p ｜u｜p-2 u=Q（x）｜u｜Np/N-p -2u,x∈R N,where 1 〈 p 〈 N,0 ≤ μ 〈（（N-p）/p）p and Q ∈ L∞（RN）.Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity.
基金Supported by National Natural Science Foundation of China (11071198 11101347)+2 种基金Postdoctor Foundation of China (2012M510363)the Key Project in Science and Technology Research Plan of the Education Department of Hubei Province (D20112605 D20122501)
文摘The existence and multiplicity of positive solutions are studied for a class of quasi- linear elliptic equations involving Sobolev critical exponents with mixed Dirichlet-Neumann boundary conditions by the variational methods and some analytical techniques.
基金Supported by the National Natural Science Foundation of China(Grant No.11626038)
文摘In this paper, we establish the existence of three weak solutions for quasilinear elliptic equations in an Orlicz-Sobolev space via an abstract result recently obtained by Ricceri in [13].
文摘The article proved the existence of H<sup>1</sup> （R） ∩ L<sup>∞</sup> （R<sup>n</sup>） at the bifurcation λ= 0 by discussing the following nonlinear eigenvalue:—D-（ij）(a<sub>ij</sub>（x,u）D<sub>j</sub>u) +1/2a<sub>iju</sub>（x,u）D<sub>i</sub>uD<sub>j</sub>u — q（x）|u|<sup>σ</sup>u = λu0≠u∈H<sup>1</sup>（R<sup>n</sup>） ,0【σ【 4/n,n≥3,x∈ R<sup>n</sup>Meanwhile the article studied the conditions of q（x） under which λ=0 was a bifurcation point for the nonlinear eigenvalue . Here a<sub>ij</sub> are not required to be bounded as u varies.
基金supported by the Natural Science Foundation of Henan Province(15A110050)
文摘In this article, we consider existence and nonexistence of solutions to problem {-△pu＋g（x,u）｜↓△｜^p=f in -Ω,u=0 on Ω with 1〈p〈∞ where f is a positive measurable function which is bounded away from 0 in Ω, and the domain Ω is a smooth bounded open set in R^N（N≥2）. Especially, under the condition that g（x, s） = 1/｜s｜^α （α〉0） is singular at s = 0, we obtain that α 〈 p is necessary and sufficient for the existence of solutions in W0^1,p（Ω） to problem （0.1） when f is sufficiently regular.
文摘We prove the existence of a ground state solution for the qusilinear elliptic equation in , under suitable conditions on a locally Holder continuous non-linearity , the non-linearity may exhibit a singularity as . We also prove the non-existence of radially symmetric solutions to the singular elliptic equation in , as where .
文摘The existence ofpositive radialsolutions ofthe equation - div(｜Du｜p- 2Du)= f(u) is studied in annular dom ains in Rn,n≥2. Itisproved thatiff(0)≥0, f is somewhere negativein (0,∞), lim u→0+ f′(u)= 0and lim u→∞(f(u)/up- 1)= ∞, then thereisa largepositiveradialsolution on allannuli.Iff(0)< 0 and satisfiescertain condi- tions, then the equation has no radialsolution ifthe annuliare too wide.
文摘In this paper, the existence and nonexistence of nonnegative entire large solutions for the quasilinear elliptic equation are established, where , and are nondecreasing and vanish at the origin. The locally H lder continuous functions and are nonnegative. We extend results previously obtained for special cases of and g.
基金supported by NSFC-Tian Yuan Special Foundation(11226116)Natural Science Foundation of Jiangsu Province of China for Young Scholar(BK2012109)+3 种基金the China Scholarship Council(201208320435)the Fundamental Research Funds for the Central Universities(JUSRP11118)supported by NSFC(10871096)supported by Graduate Education Innovation of Jiangsu Province(CXZZ13-0389)
