Multiplicity of critical orbits to nonlinear, strongly indefinite functionals with sign-changing nonlinear part
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866908408313020416 |
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| author | Bernini, Federico Bieganowski, Bartosz Strzelecki, Daniel |
| author_facet | Bernini, Federico Bieganowski, Bartosz Strzelecki, Daniel |
| contents | We show an abstract critical point theorem about existence of infinitely many critical orbits to strongly indefinite functionals with sign-changing nonlinear part defined on a dislocation space with a discrete group action. We apply the abstract result to a Schrödinger equation $$ -Δu + V(x) u = f(u) - λg(u) $$ with $0$ in the spectral gap of the Schrödinger operator $-Δ+ V(x)$, that appears in nonlinear optics, as well as to the equations with singular potentials arising from the study of cylindrically symmetric, electromagnetic waves to the system of Maxwell equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13315 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multiplicity of critical orbits to nonlinear, strongly indefinite functionals with sign-changing nonlinear part Bernini, Federico Bieganowski, Bartosz Strzelecki, Daniel Analysis of PDEs 35Q55, 35A15, 35J20, 35Q60, 58E05 We show an abstract critical point theorem about existence of infinitely many critical orbits to strongly indefinite functionals with sign-changing nonlinear part defined on a dislocation space with a discrete group action. We apply the abstract result to a Schrödinger equation $$ -Δu + V(x) u = f(u) - λg(u) $$ with $0$ in the spectral gap of the Schrödinger operator $-Δ+ V(x)$, that appears in nonlinear optics, as well as to the equations with singular potentials arising from the study of cylindrically symmetric, electromagnetic waves to the system of Maxwell equations. |
| title | Multiplicity of critical orbits to nonlinear, strongly indefinite functionals with sign-changing nonlinear part |
| topic | Analysis of PDEs 35Q55, 35A15, 35J20, 35Q60, 58E05 |
| url | https://arxiv.org/abs/2410.13315 |