在这篇论文，作者学习单个 p 拉普拉斯算符方程 −∆<sub> p </sub 的积极解决方案的存在和不存在 > 在 R <sup 的 u = f (x) u <sup>−α</sup>+λg (x) u <...在这篇论文，作者学习单个 p 拉普拉斯算符方程 −∆<sub> p </sub 的积极解决方案的存在和不存在 > 在 R <sup 的 u = f (x) u <sup>−α</sup>+λg (x) u <sup>β</sup>> N </sup> ；在哪儿 N ≥
3， 1 【
p 【
N， λ
】
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α
【
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β
+ 1 【
p *= 。我们证明那在那里存在批评价值¤以便这个问题有至少二个答案如果 0 【
λ
【
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=Λ；并且没有答案如果 λ
】
Λ
。展开更多
The existence of an infinite sequence of sign-changing solutions are proved for a class of quasilinear elliptic equations under suitable conditions on the quasilinear coefficients and the nonlinearity ■on aΩ ,where...The existence of an infinite sequence of sign-changing solutions are proved for a class of quasilinear elliptic equations under suitable conditions on the quasilinear coefficients and the nonlinearity ■on aΩ ,where Ω∈ C RN is a bounded domain with smooth boundary,and we use du 2u d D;u=x,Dju=;dxjdxj and D2bj;(z)=;bj(2).The main interest of this paper is for the case of bounded quasilinearity bj.The result is proved by an elliptic regularization method involving truncations of both u and the gradient of u.展开更多
基金The authors would like to thank the referee for carefully reading the paper and for helpful suggestions.The work is partially supported by NSFC(Nos.11761082,11671364,11771324 and 11831009).
文摘The existence of an infinite sequence of sign-changing solutions are proved for a class of quasilinear elliptic equations under suitable conditions on the quasilinear coefficients and the nonlinearity ■on aΩ ,where Ω∈ C RN is a bounded domain with smooth boundary,and we use du 2u d D;u=x,Dju=;dxjdxj and D2bj;(z)=;bj(2).The main interest of this paper is for the case of bounded quasilinearity bj.The result is proved by an elliptic regularization method involving truncations of both u and the gradient of u.
