A minimax theorem for locally Lipschitz functionals and applications

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发表日期：

2024年9月12日

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Marcelo F. Furtado,
João Pablo P. Da Silva

摘要

We prove an abstract theorem which provides multiple critical points for locally Lipschtiz functionals under the presence of symmetry. The abstract result is applied to find multiple solutions in H ₀ ¹ (Ω) for the critical semi-linear elliptic equation − Δu = f(x, u) + ∣u∣^4/(N−2)u, where f is a discontinuous perturbation and Ω ⊂ ℝ^N is a bounded smooth domain.