Multiplicity of Solutions on a Nehari Set in an Invariant Cone

Francesca Colasuonno; Benedetta Noris; Gianmaria Verzini

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Multiplicity of Solutions on a Nehari Set in an Invariant Cone

机译：在不变圆锥中集合的尼哈里上的解的多重性

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For 1 < p < 2 and q large, we prove the existence of two positive, nonconstant, radial and radially nondecreasing solutions of the supercritical equation -Δ_pu + u~(p-1) = u~(q-1) under Neumann boundary conditions, in the unit ball of ?~N. We use a variational approach in an invariant cone. We distinguish the two solutions upon their energy: one is a ground state inside a Nehari-type subset of the cone, the other is obtained via a mountain pass argument inside the Nehari set. As a byproduct of our proofs, we detect the limit profile of the low energy solution as q → ∞and show that the constant solution 1 is a local minimizer on the Nehari set. This marks a strong difference with the case p ≥ 2.

机译：1 < p < 2,问大,我们证明存在两个积极的、非常数的径向和径向不减少的超临界的解决方案方程——Δ_pu + u ~ (p - 1) = u ~ (q1)诺伊曼边界条件的单位球? ~ N。在一个不变的锥使用变分方法。我们区分两种解决方案在他们能源:一个是基态内Nehari-type锥的子集,另一个是获得通过山口参数内当地集。检测的低能量的极限解决方案为q→∞,表明该常数解决方案1在当地是一个局部最小值集。

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来源
《Minimax theory and its applications》 |2022年第2期|185-206|共22页
作者
Francesca Colasuonno; Benedetta Noris; Gianmaria Verzini;
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作者单位

Dipartimento di Matematica, Politecnico di Milano, Italy;

Dipartimento di Matematica, Università di Bologna, Italy;

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正文语种英语
中图分类数值分析;
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Multiplicity of Solutions on a Nehari Set in an Invariant Cone

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