Abstract
We consider a semilinear problem of the type $Lu=f(b,u),$ where $f(b,u)\simeq bu$ as $u\to 0$ and $f(b,u)\simeq b_\infty u$ as $\|u \| \to\infty$ assuming that there exist a finite number of eigenvalues of the linear operator $L$ between $b$ and $b_\infty$. Under suitable assumptions we prove the existence of four nontrivial solutions for $b$ close to an eigenvalue. We give an application to problems of oscillations of a forced beam.
Citation
A. M. Micheletti. C. Saccon. "Multiple solutions for an asymptotically linear problem with nonlinearity crossing a finite number of eigenvalues and application to a beam equation." Adv. Differential Equations 7 (10) 1193 - 1214, 2002. https://doi.org/10.57262/ade/1356651634
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