| Title | A NEW THEME IN NONLINEAR ANALYSIS: CONTINUATION AND BIFURCATION OF THE UNIT EIGENVECTORS OF A PERTURBED LINEAR OPERATOR |
| Publication Type | Journal Article |
| Year of Publication | 2011 |
| Authors | CHIAPPINELLI, RAFFAELE, FURI, MASSIMO, PERA, MARIAPATRIZIA |
| Secondary Title | Communications in Applied Analysis |
| Volume | 15 |
| Issue | 3 |
| Start Page | 299 |
| Pagination | 312 |
| Date Published | 08/2011 |
| Type of Work | scientific: mathematics |
| ISSN | 1083–2564 |
| AMS | 47A55, 47J05, 47J10, 47J15, 47J30 |
| Abstract | We review some recent results concerning nonlinear eigenvalue problems of the form (∗) Au + eB(u) = δu, where A is a linear Fredholm operator of index zero (with nontrivial kernel Ker A) acting in a real Banach space X, and B : X → X is a (possibly) nonlinear perturbation term. We seek solutions u of (∗) in the unit sphere S of X, and the emphasis is put on the existence - under appropriate conditions on B - of points u 0 ∈ S ∩ Ker A (thus satisfying (∗) for e = δ = 0) which either can be continued as solutions of (∗) for e = 0 or - more generally - are bifurcation points for solutions of that kind.
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| URL | http://www.acadsol.eu/en/articles/15/3/3.pdf |
| Short Title | CONTINUATION AND BIFURCATION |
| Refereed Designation | Refereed |
| Full Text | REFERENCES[1] Brown R. F., The Lefschetz Fixed Point Theorem, Scott and Foresman, 1971.
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