Displaying similar documents to “Nonlinear eigenvalue problems for fourth order ordinary differential equations”

Bifurcation theorems of Rabinowitz type for certain differential operators of the fourth order

Jolanta Przybycin (1992)

Annales Polonici Mathematici

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This paper was inspired by the works of P. H. Rabinowitz. We study nonlinear eigenvalue problems for some fourth order elliptic partial differential equations with nonlinear perturbation of Rabinowitz type. We show the existence of an unbounded continuum of nontrivial positive solutions bifurcating from (μ₁,0), where μ₁ is the first eigenvalue of the linearization about 0 of the considered problem. We also prove the related theorem for bifurcation from infinity. The results obtained...

Three methods for the study of semilinear equations at resonance

Bogdan Przeradzki (1993)

Colloquium Mathematicae

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Three methods for the study of the solvability of semilinear equations with noninvertible linear parts are compared: the alternative method, the continuation method of Mawhin and a new perturbation method [22]-[27]. Some extension of the last method and applications to differential equations in Banach spaces are presented.

Nonsymmetric solutions of a nonlinear boundary value problem

Sámuel Peres (2014)

Czechoslovak Mathematical Journal

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We study the existence and multiplicity of positive nonsymmetric and sign-changing nonantisymmetric solutions of a nonlinear second order ordinary differential equation with symmetric nonlinear boundary conditions, where both of the nonlinearities are of power type. The given problem has already been studied by other authors, but the number of its positive nonsymmetric and sign-changing nonantisymmetric solutions has been determined only under some technical conditions. It was a long-standing...