The existence of infinitely many solutions of the following Dirichlet problem for p-mean curvature operator:-div((1+|u| 2) p-22u)=f(x,u),\ x∈Ω, u∈W 1,p 0(Ω),is considered, where Ω is a bounded domain in ...The existence of infinitely many solutions of the following Dirichlet problem for p-mean curvature operator:-div((1+|u| 2) p-22u)=f(x,u),\ x∈Ω, u∈W 1,p 0(Ω),is considered, where Ω is a bounded domain in R n(n>p>1) with smooth boundary Ω.Under some natural conditions together with some conditions weaker than (AR) condition,we prove that the above problem has infinitely many solutions by a symmetric version of the Mountain Pass Theorem if f(x,u)|u| p-2u→+∞ as u→∞.展开更多
这份报纸与批评 exponent:-div 涉及p想弯曲操作员的下列 Dirichlet 问题的积极解决方案的存在((1+|() u|2 )p-2/2() u ) =up * -1+uq-1,u = 0 ， x (a) u W1 ，p0()，是在 RN 的围住的域( N p 1 )与光滑的边界(a)， 2 p q p *， ...这份报纸与批评 exponent:-div 涉及p想弯曲操作员的下列 Dirichlet 问题的积极解决方案的存在((1+|() u|2 )p-2/2() u ) =up * -1+uq-1,u = 0 ， x (a) u W1 ，p0()，是在 RN 的围住的域( N p 1 )与光滑的边界(a)， 2 p q p *， p *= Np/N-p ，， 0 。它得出这个问题在不同盒子中有至少一个积极答案的结论。它被讨论为有由第一使用 Nehari 类型两重性性质的批评代表的 p 想弯曲操作员的 Dirichlet 问题的积极答案的存在。作为 p = 2， q = p，结果是对应于 Laplace 的操作员。展开更多
基金Supported by the National Natural Science Foundation of China(1 0 1 71 0 3 2 ) and the GuangdongProvincial Natural Science Foundation(0 1 1 6 0 6 )
文摘The existence of infinitely many solutions of the following Dirichlet problem for p-mean curvature operator:-div((1+|u| 2) p-22u)=f(x,u),\ x∈Ω, u∈W 1,p 0(Ω),is considered, where Ω is a bounded domain in R n(n>p>1) with smooth boundary Ω.Under some natural conditions together with some conditions weaker than (AR) condition,we prove that the above problem has infinitely many solutions by a symmetric version of the Mountain Pass Theorem if f(x,u)|u| p-2u→+∞ as u→∞.
基金Supported by the National Natural Science Foundation of China（10171032） Supported by the Guangdong Provincial Natural Science Foundation of China（011606）
文摘这份报纸与批评 exponent:-div 涉及p想弯曲操作员的下列 Dirichlet 问题的积极解决方案的存在((1+|() u|2 )p-2/2() u ) =up * -1+uq-1,u = 0 ， x (a) u W1 ，p0()，是在 RN 的围住的域( N p 1 )与光滑的边界(a)， 2 p q p *， p *= Np/N-p ，， 0 。它得出这个问题在不同盒子中有至少一个积极答案的结论。它被讨论为有由第一使用 Nehari 类型两重性性质的批评代表的 p 想弯曲操作员的 Dirichlet 问题的积极答案的存在。作为 p = 2， q = p，结果是对应于 Laplace 的操作员。
