Range of semilinear operators for systems at resonance
For a vector function u: ℝ→ ℝ N we consider the system, where G: ℝ N → ℝ is a C 1 function. We are interested in finding all possible T-periodic forcing terms p(t) for which there is at least one solution. In other words, we examine the range of the semilinear operator S: H 2 per → L 2([0, T],ℝ N) g...
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Autores principales: | , |
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Formato: | Artículo publishedVersion |
Lenguaje: | Inglés |
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2012
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Materias: | |
Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_10726691_v2012_n_p_Amster |
Aporte de: |
Sumario: | For a vector function u: ℝ→ ℝ N we consider the system, where G: ℝ N → ℝ is a C 1 function. We are interested in finding all possible T-periodic forcing terms p(t) for which there is at least one solution. In other words, we examine the range of the semilinear operator S: H 2 per → L 2([0, T],ℝ N) given by, where. Writing p(t) = p̄ + p̄(t), where, we present several resultsconcerning the topological structure of the set. © 2012 Texas State University-San Marcos. |
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