Infinitely many solutions for a boundary value problem with discontinuous nonlinearities.
Infinitely many solutions for a mixed boundary value problem
The existence of infinitely many solutions for a mixed boundary value problem is established. The approach is based on variational methods.
Infinitely many solutions for systems of n two-point Kirchhoff-type boundary value problems
Using Ricceri's variational principle, we establish the existence of infinitely many solutions for a class of two-point boundary value Kirchhoff-type systems.
Infinitely many solutions of a second-order -Laplacian problem with impulsive condition
Using the critical point theory and the method of lower and upper solutions, we present a new approach to obtain the existence of solutions to a -Laplacian impulsive problem. As applications, we get unbounded sequences of solutions and sequences of arbitrarily small positive solutions of the -Laplacian impulsive problem.
Influence of time delays on the Hahnfeldt et al. angiogenesis model dynamics
We study the influence of time delays on the dynamics of the general Hahnfeldt et al. model of an angiogenesis process. We analyse the dynamics of the system for different values of the parameter α which reflects the strength of stimulation of the vessel formation process. Time delays are introduced in three subprocesses: tumour growth, stimulation and inhibition of vessel formation (represented by endothelial cell dynamics). We focus on possible destabilisation of the positive steady state due...
Influence of Vibrations on Convective Instability of Reaction Fronts in Liquids
Propagation of polymerization fronts with liquid monomer and liquid polymer is considered and the influence of vibrations on critical conditions of convective instability is studied. The model includes the heat equation, the equation for the concentration and the Navier-Stokes equations considered under the Boussinesq approximation. Linear stability analysis of the problem is fulfilled, and the convective instability boundary is found depending on...
Inhomogeneous linear differential equations in Banach spaces
Initial and Boundary Value Problems for Functional Differential Equations via the Topological Transversality Method: A Survey
Initial and boundary value problems for functional integro-differential equations.
Initial and boundary value problems for nonconvex valued multivalued functional differential equations.
Initial boundary value problem for the mKdV equation on a finite interval
We analyse an initial-boundary value problem for the mKdV equation on a finite interval by expressing the solution in terms of the solution of an associated matrix Riemann-Hilbert problem in the complex -plane. This RH problem is determined by certain spectral functions which are defined in terms of the initial-boundary values at and . We show that the spectral functions satisfy an algebraic “global relation” which express the implicit relation between all boundary values in terms of spectral...
Initial boundary value problems for second order impulsive functional differential inclusions.
Initial value parameters corresponding to positive Green's functions
Initial Value Problem for Mixed-Type Differential Equations.
Initial value problems for fractional functional differential inclusions with Hadamard type derivative
We establish sufficient conditions for the existence of solutions of a class of fractional functional differential inclusions involving the Hadamard fractional derivative with order . Both cases of convex and nonconvex valued right hand side are considered.
Initial value problems for nonlinear nonresonant delay differential equations with possibly infinite delay.
Initial-value methods for computing eigenvalues of two point boundary value problem
In-phase and antiphase complete chaotic synchronization in symmetrically coupled discrete maps.
Input-output systems in Biology and Chemistry and a class of mathematical models describing them
Our aim is to show a class of mathematical models in application to some problems of cell biology. Typically, our models are described via classical chemical networks. This property is visualized by a conservation law. Mathematically, this conservation law guarantees most of the mathematical properties of the models such as global existence and uniqueness of solutions as well as positivity of the solutions for positive data. These properties are consequences of the fact that the infinitesimal generators...
Input-to-state stability of neutral type systems
We consider the system (ẋ(t) ≡ dx(t)/dt), where x(t) is the state, u(t) is the input, R(τ),R̃(τ) are matrix-valued functions, and F is a causal (Volterra) mapping. Such equations enable us to consider various classes of systems from the unified point of view. Explicit input-to-state stability conditions in terms of the L²-norm are derived. Our main tool is the norm estimates for the matrix resolvents, as well as estimates for fundamental solutions of the linear parts of the considered systems,...