The solutions of the series-like iterative equation with variable coefficients.
The distance between fixed points of some pairs of maps in Banach spaces and applications to differential systems
Let be a -contraction on a Banach space and let be an almost -contraction, i.e. sum of an -contraction with a continuous, bounded function which is less than in norm. According to the contraction principle, there is a unique element in for which If moreover there exists in with , then we will give estimates for Finally, we establish some inequalities related to the Cauchy problem.
The existence of countably many positive solutions for nonlinear th-order three-point boundary value problems.
The existence of multiple positive solutions of -Laplacian boundary value problems
The existence of positive solution to a nonlinear fractional differential equation with integral boundary conditions.
The existence of positive solutions for nonlinear boundary system with -Laplacian operator based on sign-changing nonlinearities.
The existence of positive solutions for third-order -Laplacian -point boundary value problems with sign changing nonlinearity on time scales.
The fixed point theorem and the boundedness of solutions of differential equations in the Banach space
The properties of solutions of the nonlinear differential equation in a Banach space and of the special case of the homogeneous linear differential equation are studied. Theorems and conditions guaranteeing boundedness of the solution of the nonlinear equation are given on the assumption that the solutions of the linear homogeneous equation have certain properties.
The Hopf bifurcation theorem for parabolic equations with infinite delay
The existence of the Hopf bifurcation for parabolic functional equations with delay of maximum order in spatial derivatives is proved. An application to an integrodifferential equation with a singular kernel is given.
The iterative method of generalized -concave operators.
The method of subsuper solutions for weighted -Laplacian equation boundary value problems.
The periodic problem for semilinear differential inclusions in Banach spaces
Sufficient conditions on the existence of periodic solutions for semilinear differential inclusions are given in general Banach space. In our approach we apply the technique of the translation operator along trajectories. Due to recent results it is possible to show that this operator is a so-called decomposable map and thus admissible for certain fixed point index theories for set-valued maps. Compactness conditions are formulated in terms of the Hausdorff measure of noncompactness.
The Role of Green’s Functions in Inverse Scattering at Fixed Energy
Three periodic solutions for a class of higher-dimensional functional differential equations with impulses
By using the well-known Leggett–Williams multiple fixed point theorem for cones, some new criteria are established for the existence of three positive periodic solutions for a class of n-dimensional functional differential equations with impulses of the form ⎧y’(t) = A(t)y(t) + g(t,yt), , j ∈ ℤ, ⎨ ⎩, where is a nonsingular matrix with continuous real-valued entries.
Three positive solutions for a system of singular generalized Lidstone problems.
Three positive solutions for -Laplacian functional dynamic equations on time scales.
Time-scale-dependent criteria for the existence of positive solutions to -Laplacian multipoint boundary value problem.
Trichotomy and bounded solutions of nonlinear differential equations
The existence of bounded solutions for equations in Banach spaces is proved. We assume that the linear part is trichotomic and the perturbation satisfies some conditions expressed in terms of measures of noncompactness.
Triple positive solutions for a boundary value problem of nonlinear fractional differential equation.
Triple positive solutions for a type of second-order singular boundary problems.