Existence and bifurcation of solutions for Fredholm operators with nonlinear perturbations

In this paper we shall discuss nonlinear eigenvalue problems for the equations of the formwhere L is a linear operator on a real Banach space X with non-zero kernel, K(-) is a linear or nonlinear operator on X and M(·, ·) is an operator from X X R into X. Equations of the form (1) arise in various fields of physics and engineering.

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Global bifurcation of solutions of certain nonlinear eigenvalue problems for ordinary differential equations of fourth order

Sbornik Mathematics ◽

10.1070/sm8369 ◽

2016 ◽

Vol 207 (12) ◽

pp. 1625-1649 ◽

Cited By ~ 4

Author(s):

Z S Aliyev

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Fourth Order ◽

Eigenvalue Problems ◽

Global Bifurcation ◽

Nonlinear Eigenvalue Problems ◽

Bifurcation Of Solutions ◽

Nonlinear Eigenvalue

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Existence of Solution for Some Nonlinear Eigenvalue Problems

Diyala Journal for Pure Science ◽

10.24237/djps.1404.452a ◽

2018 ◽

Vol 14 (4) ◽

pp. 88-104

Author(s):

Fatima Mohammed Aboud ◽

Keyword(s):

Eigenvalue Problems ◽

Existence Of Solution ◽

Nonlinear Eigenvalue Problems ◽

Nonlinear Eigenvalue

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A large-grained parallel algorithm for nonlinear eigenvalue problems and its implementation using OmniRPC

2008 IEEE International Conference on Cluster Computing ◽

10.1109/clustr.2008.4663754 ◽

2008 ◽

Cited By ~ 1

Author(s):

Takeshi Amako ◽

Yusaku Yamamoto ◽

Shao-Liang Zhang

Keyword(s):

Parallel Algorithm ◽

Eigenvalue Problems ◽

Nonlinear Eigenvalue Problems ◽

Nonlinear Eigenvalue

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Nodal solutions to nonlinear eigenvalue problems on time scales

Nonlinear Analysis ◽

10.1016/j.na.2005.09.043 ◽

2006 ◽

Vol 65 (4) ◽

pp. 773-784 ◽

Cited By ~ 5

Author(s):

Hua Luo ◽

Ruyun Ma

Keyword(s):

Time Scales ◽

Eigenvalue Problems ◽

Nodal Solutions ◽

Nonlinear Eigenvalue Problems ◽

Nonlinear Eigenvalue

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MULTIPLE POSITIVE SOLUTIONS OF NONLINEAR EIGENVALUE PROBLEMS ASSOCIATED TO A CLASS OF p-LAPLACIAN LIKE OPERATORS

Communications in Contemporary Mathematics ◽

10.1142/s0219199703001105 ◽

2003 ◽

Vol 05 (05) ◽

pp. 737-759 ◽

Cited By ~ 4

Author(s):

NOBUYOSHI FUKAGAI ◽

KIMIAKI NARUKAWA

Keyword(s):

Positive Solutions ◽

Elliptic Problem ◽

Eigenvalue Problems ◽

Multiple Positive Solutions ◽

Combined Effects ◽

Nonlinear Eigenvalue Problems ◽

Quasilinear Elliptic Problem ◽

Quasilinear Elliptic ◽

Nonlinear Eigenvalue

This paper deals with positive solutions of a class of nonlinear eigenvalue problems. For a quasilinear elliptic problem (#) - div (ϕ(|∇u|)∇u) = λf(x,u) in Ω, u = 0 on ∂Ω, we assume asymptotic conditions on ϕ and f such as ϕ(t) ~ tp0-2, f(x,t) ~ tq0-1as t → +0 and ϕ(t) ~ tp1-2, f(x,t) ~ tq1-1as t → ∞. The combined effects of sub-nonlinearity (p0> q0) and super-nonlinearity (p1< q1) with the subcritical term f(x,u) imply the existence of at least two positive solutions of (#) for 0 < λ < Λ.

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Finite element methods for nonlinear eigenvalue problems and the postbuckling behavior of elastic plates

Computers & Structures ◽

10.1016/0045-7949(76)90020-1 ◽

1976 ◽

Vol 6 (4-5) ◽

pp. 413-418 ◽

Cited By ~ 21

Author(s):

L.Carter Wellford ◽

Ghassan M. Dib

Keyword(s):

Finite Element ◽

Finite Element Methods ◽

Eigenvalue Problems ◽

Elastic Plates ◽

Postbuckling Behavior ◽

Nonlinear Eigenvalue Problems ◽

Nonlinear Eigenvalue

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On Ricceri’s conjecture for a class of nonlinear eigenvalue problems

Applied Mathematics Letters ◽

10.1016/j.aml.2009.03.012 ◽

2009 ◽

Vol 22 (9) ◽

pp. 1386-1389 ◽

Cited By ~ 4

Author(s):

Xianling Fan

Keyword(s):

Eigenvalue Problems ◽

Nonlinear Eigenvalue Problems ◽

Nonlinear Eigenvalue

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Iterations converging to distinct solutions of some nonlinear operator equations in Banach space

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s016117128600073x ◽

1986 ◽

Vol 9 (3) ◽

pp. 583-587

Author(s):

Ioannis K. Argyros

Keyword(s):

Banach Space ◽

Linear Operator ◽

Nonlinear Operator ◽

Operator Equations ◽

Nonlinear Operator Equations

We examine the solvability of multilinear equations of the formMk(x,x,…,x)−k times−=y, k=2,3,…whereMkis ak-linear operator on a Banach spaceXandy∈Xis fixed.

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