Degeneracy in the Blasius problem.
Degree of convergence of iterative algorithms for boundedly Lipschitzian strong pseudocontractions.
Demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces.
Dependence results on almost periodic and almost automorphic solutions of evolution equations.
Destabilization for quasivariational inequalities of reaction-diffusion type
We consider a reaction-diffusion system of the activator-inhibitor type with unilateral boundary conditions leading to a quasivariational inequality. We show that there exists a positive eigenvalue of the problem and we obtain an instability of the trivial solution also in some area of parameters where the trivial solution of the same system with Dirichlet and Neumann boundary conditions is stable. Theorems are proved using the method of a jump in the Leray-Schauder degree.
Die Lösung der Verzweigungsgleichungen für nichtlineare Eigenwertprobleme.
Directional contractors and equations in Banach spaces
Dirichlet problems without convexity assumption
We deal with the existence of solutions of the Dirichlet problem for sublinear and superlinear partial differential inclusions considered as generalizations of the Euler-Lagrange equation for a certain integral functional without convexity assumption. We develop a duality theory and variational principles for this problem. As a consequence of the duality theory we give a numerical version of the variational principles which enables approximation of the solution for our problem.
Diskrete Approximation von Eigenwertproblemen. I. Qualitative Konvergenz.
Diskrete Approximation von Eigenwertproblemen. II. Konvergenzordnung.
Diskrete Approximation von Eigenwertproblemen. III. Asymptotische Entwicklungen. - Discrete Approximation of Eigenvalue-Problems. III. Asymptotic Expansions.
Dissipative sets and nonlinear perturbated equations in Banach spaces
Does Newton's method for set-valued maps converges uniformly in mild differentiability context?
Dual convergences of iteration processes for nonexpansive mappings in Banach spaces
In this paper we establish a dual weak convergence theorem for the Ishikawa iteration process for nonexpansive mappings in a reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm, and then apply this result to study the problem of the weak convergence of the iteration process.
Dynamical problems without initial conditions for elliptic-parabolic equations in spatial unbounded domains.
Dynamics of a modified Davey-Stewartson system in ℝ³
We study the Cauchy problem in ℝ³ for the modified Davey-Stewartson system , . Under certain conditions on λ₁ and λ₂, we provide a complete picture of the local and global well-posedness, scattering and blow-up of the solutions in the energy space. Methods used in the paper are based upon the perturbation theory from [Tao et al., Comm. Partial Differential Equations 32 (2007), 1281-1343] and the convexity method from [Glassey, J. Math. Phys. 18 (1977), 1794-1797].
Dynamics of systems with Preisach memory near equilibria
We consider autonomous systems where two scalar differential equations are coupled with the input-output relationship of the Preisach hysteresis operator, which has an infinite-dimensional memory. A prototype system of this type is an LCR electric circuit where the inductive element has a ferromagnetic core with a hysteretic relationship between the magnetic field and the magnetization. Further examples of such systems include lumped hydrological models with two soil layers; they can also appear...
Eigenvalue problems and bifurcation of nonhomogeneous semilinear elliptic equations in exterior strip domains.
Eigenvalue problems for a quasilinear elliptic equation on .
Eigenvalue results for pseudomonotone perturbations of maximal monotone operators
Let X be an infinite-dimensional real reflexive Banach space such that X and its dual X* are locally uniformly convex. Suppose that T: X⊃D(T) → 2X* is a maximal monotone multi-valued operator and C: X⊃D(C) → X* is a generalized pseudomonotone quasibounded operator with L ⊂ D(C), where L is a dense subspace of X. Applying a recent degree theory of Kartsatos and Skrypnik, we establish the existence of an eigensolution to the nonlinear inclusion 0 ∈ T x + λ C x, with a regularization method by means...