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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.

Some global results for nonlinear Sturm-Liouville problems with spectral parameter in the boundary condition

Ziyatkhan S. Aliyev, Gunay M. Mamedova (2015)

Annales Polonici Mathematici

We consider nonlinear Sturm-Liouville problems with spectral parameter in the boundary condition. We investigate the structure of the set of bifurcation points, and study the behavior of two families of continua of nontrivial solutions of this problem contained in the classes of functions having oscillation properties of the eigenfunctions of the corresponding linear problem, and bifurcating from the points and intervals of the line of trivial solutions.

Some new oscillation criteria for second order elliptic equations with damping

Rong-Kun Zhuang, Zheng-an Yao (2005)

Annales Polonici Mathematici

Some new oscillation criteria are obtained for second order elliptic differential equations with damping i , j = 1 n D i [ A i j ( x ) D j y ] + i = 1 n b i ( x ) D i y + q ( x ) f ( y ) = 0 , x ∈ Ω, where Ω is an exterior domain in ℝⁿ. These criteria are different from most known ones in the sense that they are based on the information only on a sequence of subdomains of Ω ⊂ ℝⁿ, rather than on the whole exterior domain Ω. Our results are more natural in view of the Sturm Separation Theorem.

Some notes on oscillation of two-dimensional system of difference equations

Zdeněk Opluštil (2014)

Mathematica Bohemica

Oscillatory properties of solutions to the system of first-order linear difference equations Δ u k = q k v k Δ v k = - p k u k + 1 , are studied. It can be regarded as a discrete analogy of the linear Hamiltonian system of differential equations. We establish some new conditions, which provide oscillation of the considered system. Obtained results extend and improve, in certain sense, results presented in Opluštil (2011).

Some observations on a Conti's result

Adrian Constantin (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

An extension of a result of R. Conti is given from which some integro-differential inequalities of the Gronwall-Bellman-Bihari type and a criterion for the continuation of solutions of a system of ordinary differential equations are deduced.

Some oscillation theorems for second order differential equations

Chung-Fen Lee, Cheh Chih Yeh, Chuen-Yu Gau (2005)

Czechoslovak Mathematical Journal

In this paper we establish some oscillation or nonoscillation criteria for the second order half-linear differential equation ( r ( t ) Φ ( u ' ( t ) ) ) ' + c ( t ) Φ ( u ( t ) ) = 0 , where (i) r , c C ( [ t 0 , ) , : = ( - , ) ) and r ( t ) > 0 on [ t 0 , ) for some t 0 0 ; (ii) Φ ( u ) = | u | p - 2 u for some fixed number p > 1 . We also generalize some results of Hille-Wintner, Leighton and Willet.

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