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Existence results for forced nonlinear periodic BVPs at resonance

Sunto

In questo lavoro si presentano alcuni risultati riguardanti l'esistenza di soluzioni p-periodiche per sistemi di equazioni differenziali non lineari in risonanza, del tipo x″+ Dx + + Ag(t, x)=h(t), ove D ed A sono matrici m×m, con D di tipo diagonale, h è un termine forzante p-periodico e g è un campo vettoriale, non necessariamente limitato. In particolare, viene esteso ai sistemi, in ipotesi più generali, un classico teorema dovuto a Lazer e Leach. Le dimostrazioni sono basate sull'uso del grado topologico (teorema di continuazione di Mawhin).

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Omari, P., Zanolin, F. Existence results for forced nonlinear periodic BVPs at resonance. Annali di Matematica pura ed applicata 141, 127–157 (1985). https://doi.org/10.1007/BF01763171

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Keywords

  • Existence Result
  • Periodic BVPs