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arXiv · 2606.14444

Infinitely many sign-changing solutions for logarithmic Schr\"odinger equations via an \(L^p\)-perturbation approach

Chen Huang·Zhipeng Yang·Jiazheng Zhou
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Abstract

We study the logarithmic Schr\"odinger equation \[ -\Delta u+V(x)u=u\log u^2,\qquad x\in\mathbb R^N,\ N\ge3. \] Since the logarithmic energy is not \(C^1\) on the natural space \(H_V^1(\mathbb R^N)\), direct invariant-set minimax arguments for sign-changing solutions are not available. We introduce an \(L^p\)-regularization perturbation, which restores a \(C^1\) variational structure while preserving the logarithmic nonlinearity, and prove via a limiting argument that the original equation admits infinitely many sign-changing weak solutions.

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Chen Huang, Zhipeng Yang, Jiazheng Zhou. 2026-06-12. Infinitely many sign-changing solutions for logarithmic Schr\"odinger equations via an \(L^p\)-perturbation approach. https://arxiv.org/abs/2606.14444

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