On the behavior of the ground state energy under weak perturbation of critical quasilinear operators in $\mathbb{R}^N$

Ujjal Das; Hynek Kovařík; Yehuda Pinchover

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arXiv · 2508.01940

On the behavior of the ground state energy under weak perturbation of critical quasilinear operators in $\mathbb{R}^N$

Ujjal Das·Hynek Kovařík·Yehuda Pinchover

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Abstract

We consider a critical quasilinear operator $-\Delta_p u +V|u|^{p-2}u$ in $\mathbb{R}^N$ perturbed by a weakly coupled potential. For $N>p$, we find the leading asymptotic of the lowest eigenvalue of such an operator in the weak coupling limit separately for $N>p^2$ and $N\leq p^2$.

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Ujjal Das, Hynek Kovařík, Yehuda Pinchover. 2025-08-03. On the behavior of the ground state energy under weak perturbation of critical quasilinear operators in $\mathbb{R}^N$. https://arxiv.org/abs/2508.01940

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