6533b7d2fe1ef96bd125f3f5

RESEARCH PRODUCT

Lacunary Bifurcation of Multiple Solutions of Nonlinear Eigenvalue Problems

Hans-peter Heinz

subject

PhysicsLinear mapsymbols.namesakePure mathematicsDual spacePairingNorm (mathematics)Scalar (mathematics)Hilbert spacesymbolsLacunary functionEigenvalues and eigenvectors

description

In order to describe the type of nonlinear eigenvalue problems we are going to discuss, consider a densely defined closed linear operator T in a real Hilbert space H and let H1 be the Hilbert space which consists of the domain of T together with the graph norm. Also, let H 1 * be the dual space of H1 and denote the dual operator corresponding to T: H1 → H by T’:H → H 1 * . Since H1 is dense in H, we may view H as a subspace of H1, and then the scalar product (·,·) on H and the dual pairing on H1 × H 1 * coincide on H1 × H.

yearjournalcountryeditionlanguage
1991-01-01
https://doi.org/10.1007/978-3-0348-7004-7_19