6533b7d5fe1ef96bd126504b

RESEARCH PRODUCT

Existence and gap-bifurcation of multiple solutions to certain nonlinear eigenvalue problems

Hans-peter Heinz

subject

Pure mathematicsApplied MathematicsMathematical analysisHilbert spaceNonlinear systemsymbols.namesakeBounded functionNorm (mathematics)symbolsSpectral gapDivide-and-conquer eigenvalue algorithmAnalysisSelf-adjoint operatorEigenvalues and eigenvectorsMathematics

description

IN THIS PAPER we study: (i) a class of operator equations in an abstract Hilbert space; and (ii) the L2-theory of certain nonlinear Schrodinger equations which can be viewed as special cases of (i). In order to describe the type of abstract nonlinear eigenvalue problems to be discussed, consider a real Hilbert space H with scalar product (* , *) and norm II.11 and let S be a (not necessarily bounded) positive self-adjoint linear operator in li. We write S in the form

yearjournalcountryeditionlanguage
1993-09-01Nonlinear Analysis: Theory, Methods & Applications
https://doi.org/10.1016/0362-546x(93)90128-f