On some application of the Bochenek theorem.
On some modification of the Levinson operator and its application to a three-point boundary value problem
On some nonlinear alternatives of Leray-Schauder type and functional integral equations
In this paper, some new fixed point theorems concerning the nonlinear alternative of Leray-Schauder type are proved in a Banach algebra. Applications are given to nonlinear functional integral equations in Banach algebras for proving the existence results. Our results of this paper complement the results that appear in Granas et. al. (Granas, A., Guenther, R. B. and Lee, J. W., Some existence principles in the Caratherodony theory of nonlinear differential system, J. Math. Pures Appl. 70 (1991),...
On the antimaximum principle for parabolic periodic problems with weight.
On the asymptotic integration of nonlinear dynamic equations.
On the connectedness of the set of fixed points of a compact operator in the Fréchet space
On the correct formulation of a nonlinear differential equation in Banach spaces.
On the existence and the stability of solutions for higher-order semilinear Dirichlet problems
We investigate the existence and stability of solutions for higher-order two-point boundary value problems in case the differential operator is not necessarily positive definite, i.e. with superlinear nonlinearities. We write an abstract realization of the Dirichlet problem and provide abstract existence and stability results which are further applied to concrete problems.
On the existence of a weak solution of a half-cell model for PEM fuel cells.
On the existence of blowing-up solutions for a mean field equation
On the existence of multiple solutions for a nonlocal BVP with vector-valued response
The existence of positive solutions for a nonlocal boundary-value problem with vector-valued response is investigated. We develop duality and variational principles for this problem. Our variational approach enables us to approximate solutions and give a measure of a duality gap between the primal and dual functional for minimizing sequences.
On the existence of one-signed periodic solutions of some differential equations of second order
We study the existence of one-signed periodic solutions of the equations where , is continuous and 1-periodic, is a continuous and 1-periodic in the first variable and may take values of different signs. The Krasnosielski fixed point theorem on cone is used.
On the existence of optimal controls for nonlinear infinite dimensional systems
We consider nonlinear systems with a priori feedback. We establish the existence of admissible pairs and then we show that the Lagrange optimal control problem admits an optimal pair. As application we work out in detail two examples of optimal control problems for nonlinear parabolic partial differential equations.
On the existence of solutions for dynamic boundary value problems under barrier strips condition.
On the solution set of a two point boundary value problem.
On the solution sets of some nonconvex hyperbolic differential inclusions
On the solvability of a fourth-order multi-point boundary value problem
We are concerned with the solvability of the fourth-order four-point boundary value problem ⎧ , t ∈ [0,1], ⎨ u(0) = u(1) = 0, ⎩ au”(ζ₁) - bu”’(ζ₁) = 0, cu”(ζ₂) + du”’(ζ₂) = 0, where 0 ≤ ζ₁ < ζ₂ ≤ 1, f ∈ C([0,1] × [0,∞) × (-∞,0],[0,∞)). By using Guo-Krasnosel’skiĭ’s fixed point theorem on cones, some criteria are established to ensure the existence, nonexistence and multiplicity of positive solutions for this problem.
On the solvability of a system of wave and beam equations.
On the solvability of anti-periodic boundary value problems with impulses.
On the solvability of second-order impulsive differential equations with antiperiodic boundary value conditions.