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Some global results for nonlinear fourth order eigenvalue problems

Ziyatkhan Aliyev (2014)

Open Mathematics

In this paper, we consider the nonlinear fourth order eigenvalue problem. We show the existence of family of unbounded continua of nontrivial solutions bifurcating from the line of trivial solutions. These global continua have properties similar to those found in Rabinowitz and Berestycki well-known global bifurcation theorems.

The distance between fixed points of some pairs of maps in Banach spaces and applications to differential systems

Cristinel Mortici (2006)

Czechoslovak Mathematical Journal

Let T be a γ -contraction on a Banach space Y and let S be an almost γ -contraction, i.e. sum of an ε , γ -contraction with a continuous, bounded function which is less than ε in norm. According to the contraction principle, there is a unique element u in Y for which u = T u . If moreover there exists v in Y with v = S v , then we will give estimates for u - v . Finally, we establish some inequalities related to the Cauchy problem.

The existence of solution for boundary value problems for differential equations with deviating arguments and p-Laplacian

Bing Liu, Jianshe Yu (2000)

Annales Polonici Mathematici

We consider a boundary value problem for a differential equation with deviating arguments and p-Laplacian: - ( ϕ p ( x ' ) ) ' + d / d t g r a d F ( x ) + g ( t , x ( t ) , x ( δ ( t ) ) , x’(t), x’(τ(t))) = 0, t ∈ [0,1]; x ( t ) = φ ̲ ( t ) , t ≤ 0; x ( t ) = φ ¯ ( t ) , t ≥ 1. An existence result is obtained with the help of the Leray-Schauder degree theory, with no restriction on the damping forces d/dt grad F(x).

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