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We consider the class of nonlinear eigenvalue problems (an ¡ 1 (x)(¢ ¢ ¢ (a1 (x)((a0 (x)u p 0 ¤) 0) p 1 ¤) 0 ¢ ¢ ¢) p n¡ 1 ¤) 0 = ¶ b(x)u r¤ ; where y p¤ = jyj p sgn y, p i > 0 and p0 p1 : : : pn ¡ 1 = r, with various boundary conditions. We prove the existence of eigenvalues and study the zero properties and structure of the corresponding eigenfunctions.
We consider the eigenvalue-eigenvector problem where p 1 p m?1 = r. We prove an analogue of the classical Gantmacher{Krein Theorem for the eigenvalue-eigenvector structure of STP matrices in the case where p i 1 for each i, plus various extensions thereof. A matrix A is said to be strictly totally positive (STP) if all its minors are strictly positive. STP(More)
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