On the behavior of the ground state energy under weak perturbation of critical quasilinear operators in $\mathbb{R}^N$
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| Format: | Preprint |
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2025
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| _version_ | 1866911089992663040 |
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| author | Das, Ujjal Kovařík, Hynek Pinchover, Yehuda |
| author_facet | Das, Ujjal Kovařík, Hynek Pinchover, Yehuda |
| contents | We consider a critical quasilinear operator $-Δ_p u +V|u|^{p-2}u$ 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 $N\leq p^2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_01940 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the behavior of the ground state energy under weak perturbation of critical quasilinear operators in $\mathbb{R}^N$ Das, Ujjal Kovařík, Hynek Pinchover, Yehuda Analysis of PDEs Mathematical Physics Functional Analysis Spectral Theory 35J92, 35B38, 35J10 We consider a critical quasilinear operator $-Δ_p u +V|u|^{p-2}u$ 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 $N\leq p^2$. |
| title | On the behavior of the ground state energy under weak perturbation of critical quasilinear operators in $\mathbb{R}^N$ |
| topic | Analysis of PDEs Mathematical Physics Functional Analysis Spectral Theory 35J92, 35B38, 35J10 |
| url | https://arxiv.org/abs/2508.01940 |