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Global continua of periodic solutions to some difference-differential equations of neutral type

Global continua of periodic solutions to some difference-differential equations of neutral type
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GLOBAL CONTINUA OF POSITIVE SOLUTIONS FOR SOME BOUNDARY VALUE PROBLEMS

Demonstratio Mathematica, 2002
The existence of an unbounded continuous branch of positive solutions, emanating from \(0\), is proved to Dirichlet problems for second-order linear as well as nonlinear differential equations in Banach spaces. Three theorems on global continua of positive solutions are given on the basis of the techniques developed by M. A. Krasnoselskii.
Nguyen Bich Huy, Tran Dinh Thanh
exaly   +3 more sources

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The structure of Rabinowitz' global bifurcating continua for generic quasilinear elliptic equations

Nonlinear Analysis: Theory, Methods & Applications, 1998
Global bifurcation branches for boundary value problems of the type \[ \begin{gathered} -\sum_{i,j=1}^n a_{ij}(\cdot) u_{x_ix_j}(x) + \sum_{i=1}^n b_i(\cdot) u_{x_i}(x) + c(\cdot)u(x) = \lambda d(x) u(x) + f(\lambda,\cdot) \quad \text{in } \Omega \\ u(x) = 0 \quad\text{on } \partial \Omega \end{gathered} \] are studied.
Bryan Rynne
exaly   +2 more sources

Infinitely many global continua bifurcating from a single solution of an elliptic problem with concave–convex nonlinearity

Journal of Mathematical Analysis and Applications, 2016
We study the bifurcation of solutions of semilinear elliptic boundary value problems of the form \begin{align*} \begin{aligned} -Δu &= f_λ(|x|,u,|\nabla u|) &&\text{in }Ω, u &= 0 &&\text{on }\partialΩ, \end{aligned} \end{align*} on an annulus $Ω\subset\mathbb{R}^N$, with a concave-convex nonlinearity, a special case being the ...
Thomas Bartsch, Rainer Mandel
exaly   +3 more sources

Global Formulation of Thermodynamics of Continua

1980
Throughout this paper ℝ denotes the set of all real numbers. The space E , whose elements x, y,..., we call spatial points, has the structure of a three-dimensional Euclidean point space. The translation space of E is denoted by E, and E is the set of all skew linear transformations from E into V.
G. Lebon, P. Perzyna
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Estimates of Periods and Global Continua of Periodic Solutions for State-Dependent Delay Equations

SIAM Journal on Mathematical Analysis, 2012
Consider the state-dependent delay differential equation (SDDDE) \[ x'(t) = f(x(t), x(t-\tau(t)), \sigma),\quad \tau'(t) = g(x(t), \tau(t), \sigma), \] where \(x(t) \in {\mathbb R}^N\), \(0 \leq \tau(t)
Qingwen Hu, Jianhong Wu, Xingfu Zou
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The structure of Rabinowitz' global bifurcating continua for problems with weak nonlinearities

Mathematika, 1997
Summary: Rabinowitz' global bifurcation theorem shows that for a large class of nonlinear eigenvalue problems a continuum (i.e., a closed, connected set) of solutions bifurcates from the trivial solution at each eigenvalue (or characteristic value) of odd multiplicity of the linearized problem (linearized at the trivial solution).
Bari, Rehana, Rynne, Bryan P.
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Global bifurcation and continua of nonnegative solutions for a quasilinear elliptic problem

Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 1999
In this Note, we study the existence and multiplicity of solutions, strictly positive or nonnegative having a dead core (where the solution vanishes) of a one-dimensional equation of eigenvalue type associated to a quasilinear operator with strong absorption with respect to the diffusion.
Jesús Ildefonso Díaz, Jesus Hernández
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