Let G he a hounded domain in E Consider the following quasi-linear elliptic equationAlthough the houndedness of generalized solutions of the equation is proved for very general structural conditions, it does not suppl...Let G he a hounded domain in E Consider the following quasi-linear elliptic equationAlthough the houndedness of generalized solutions of the equation is proved for very general structural conditions, it does not supply a priori estimate for maximum modulus of solutions. In this paper an estimate to the maximum modulus is made firstly for a special case of quasi-linear elliptic equations, i.e. the A and B satisfy the following structural conditions展开更多
In this paper,we study the following quasi-linear elliptic equation:■where Ω?R^(N) is a bounded domain,λ>0 is a parameter.The function ψ(|t|)t is the subcritical term,and φ(|t|)t is the critical Orlicz-Sobolev...In this paper,we study the following quasi-linear elliptic equation:■where Ω?R^(N) is a bounded domain,λ>0 is a parameter.The function ψ(|t|)t is the subcritical term,and φ(|t|)t is the critical Orlicz-Sobolev growth term with respect to φ.Under appropriate conditions on φ,ψ and φ,we prove the existence of infinitely many weak solutions for quasi-linear elliptic equation,for λ∈(0,λ_(0)),where λ_(0)> 0 is a fixed constant.展开更多
Interface problems for second order quasi-linear elliptic partial differential equations in a two-dimensional space are studied.We prove that each weak solution can be decomposed into two parts near singular points,on...Interface problems for second order quasi-linear elliptic partial differential equations in a two-dimensional space are studied.We prove that each weak solution can be decomposed into two parts near singular points,one of which is a finite sum of functions of the form cr~α log^m r(?)(θ),where the coefficients c depend on the H^1-norm of the solution,the C^(0,δ)-norm of the solution,and the equation only;and the other one of which is a regular one,the norm of which is also estimated.展开更多
We establish the existence, uniqueness and the blow-up rate of the large positive solution of the quasi-linear elliptic problem -△pu=λ（x）u^θ-1-b（x）h（u）, in Ω,with boundary condition u = ＋∞ on δΩ, where ...We establish the existence, uniqueness and the blow-up rate of the large positive solution of the quasi-linear elliptic problem -△pu=λ（x）u^θ-1-b（x）h（u）, in Ω,with boundary condition u = ＋∞ on δΩ, where Ω R^N （N≥2） is a smooth bounded domain, 1 〈 p 〈∞ λ（·） and b（·） are positive weight functions and h（u） ～ uq-1 as u → ∞. Our results extend the previous work [Z. Xie, J. Diff. Equ., 247 （2009）, 344-363] from case p = 2, λ is a constant and θ = 2 to case 1 〈 p 〈∞, A is a function and 1 （ 0 〈 θ 〈q 〉 p）; and also extends the previous work [Z. Xie, C. Zhao, J. Diff. Equ., 252 （2012）, 1776-1788], from case A is a constant and θ = p to case λ is a function and 1 〈 θ 〈 q （ 〉 p）. Moreover, we remove the assumption of radial symmetry of the problem and we do not require h（·） is increasing.展开更多
文摘Let G he a hounded domain in E Consider the following quasi-linear elliptic equationAlthough the houndedness of generalized solutions of the equation is proved for very general structural conditions, it does not supply a priori estimate for maximum modulus of solutions. In this paper an estimate to the maximum modulus is made firstly for a special case of quasi-linear elliptic equations, i.e. the A and B satisfy the following structural conditions
基金supported by National Natural Science Foundation of China (No.12101192, 11571339, 11871195,11301153)Key Scientific Research Projects of Higher Education Institutions in Henan Province(No.20B110004)。
文摘In this paper,we study the following quasi-linear elliptic equation:■where Ω?R^(N) is a bounded domain,λ>0 is a parameter.The function ψ(|t|)t is the subcritical term,and φ(|t|)t is the critical Orlicz-Sobolev growth term with respect to φ.Under appropriate conditions on φ,ψ and φ,we prove the existence of infinitely many weak solutions for quasi-linear elliptic equation,for λ∈(0,λ_(0)),where λ_(0)> 0 is a fixed constant.
基金supported by the China State Major Key Project for Basic Researchesthe Science Fund of the Ministry of Education of China
文摘Interface problems for second order quasi-linear elliptic partial differential equations in a two-dimensional space are studied.We prove that each weak solution can be decomposed into two parts near singular points,one of which is a finite sum of functions of the form cr~α log^m r(?)(θ),where the coefficients c depend on the H^1-norm of the solution,the C^(0,δ)-norm of the solution,and the equation only;and the other one of which is a regular one,the norm of which is also estimated.
基金Acknowledgments Research is partly supported by the National Science Foundation of China （10701066 ＆ 10971087）.
文摘We establish the existence, uniqueness and the blow-up rate of the large positive solution of the quasi-linear elliptic problem -△pu=λ（x）u^θ-1-b（x）h（u）, in Ω,with boundary condition u = ＋∞ on δΩ, where Ω R^N （N≥2） is a smooth bounded domain, 1 〈 p 〈∞ λ（·） and b（·） are positive weight functions and h（u） ～ uq-1 as u → ∞. Our results extend the previous work [Z. Xie, J. Diff. Equ., 247 （2009）, 344-363] from case p = 2, λ is a constant and θ = 2 to case 1 〈 p 〈∞, A is a function and 1 （ 0 〈 θ 〈q 〉 p）; and also extends the previous work [Z. Xie, C. Zhao, J. Diff. Equ., 252 （2012）, 1776-1788], from case A is a constant and θ = p to case λ is a function and 1 〈 θ 〈 q （ 〉 p）. Moreover, we remove the assumption of radial symmetry of the problem and we do not require h（·） is increasing.
