Abstract
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 10 (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 ⊂ ℝN is a bounded smooth domain.
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Furtado, M.F., Da Silva, J.P.P. A minimax theorem for locally Lipschitz functionals and applications. JAMA (2024). https://doi.org/10.1007/s11854-024-0346-z
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DOI: https://doi.org/10.1007/s11854-024-0346-z