A nonlinear bounday value problem for a nonlinear ordinary differential operator in weighted Sobolev spaces.
A priori estimates and solvability of a non-resonant generalized multi-point boundary value problem of mixed Dirichlet-Neumann-Dirichlet type involving a -Laplacian type operator
This paper is devoted to the problem of existence of a solution for a non-resonant, non-linear generalized multi-point boundary value problem on the interval . The existence of a solution is obtained using topological degree and some a priori estimates for functions satisfying the boundary conditions specified in the problem.
Ambrosetti-Prodi type results in a system of second and fourth-order ordinary differential equations.
Basis properties of eigenfunctions of nonlinear Sturm-Liouville problems.
Boundary value problems for nonlinear perturbations of some ϕ-Laplacians
This paper surveys a number of recent results obtained by C. Bereanu and the author in existence results for second order differential equations of the form (ϕ(u'))' = f(t,u,u') submitted to various boundary conditions. In the equation, ϕ: ℝ → ≤ ]-a,a[ is a homeomorphism such that ϕ(0) = 0. An important motivation is the case of the curvature operator, where ϕ(s) = s/√(1+s²). The problems are reduced to fixed point problems in suitable function space, to which Leray-Schauder...
Error analysis of Adomian series solution to a class of nonlinear differential equations.
Étude qualitative des solutions réelles d'une équation différentielle liée à l'équation de Ginzburg-Landau
Existence and location result for the bending of a single elastic beam
Existence of Periodic Solutions for Nonlinear Neutral Dynamic Equations with Functional Delay on a Time Scale
Let be a periodic time scale. The purpose of this paper is to use a modification of Krasnoselskii’s fixed point theorem due to Burton to prove the existence of periodic solutions on time scale of the nonlinear dynamic equation with variable delay , , where is the -derivative on and is the -derivative on . We invert the given equation to obtain an equivalent integral equation from which we define a fixed point mapping written as a sum of a large contraction and a compact map. We show...
Far from equilibrium steady states of 1D-Schrödinger–Poisson systems with quantum wells I
Lower bounds for eigenvalues of the one-dimensional -Laplacian.
Maximum principles and uniqueness results of phi-Laplacian boundary value problems.
New spectral criteria for almost periodic solutions of evolution equations
We present a general spectral decomposition technique for bounded solutions to inhomogeneous linear periodic evolution equations of the form ẋ = A(t)x + f(t) (*), with f having precompact range, which is then applied to find new spectral criteria for the existence of almost periodic solutions with specific spectral properties in the resonant case where may intersect the spectrum of the monodromy operator P of (*) (here sp(f) denotes the Carleman spectrum of f). We show that if (*) has a bounded...
Nonlinear discrete periodic boundary value problems at resonance.
Nonlinear systems with mean curvature-like operators
We give an existence result for a periodic boundary value problem involving mean curvature-like operators. Following a recent work of R. Manásevich and J. Mawhin, we use an approach based on the Leray-Schauder degree.
Problems with nonlinear boundary value conditions
The existence and multiplicity results are shown for certain types of problems with nonlinear boundary value conditions.
Properties of solutions of quaternionic Riccati equations
In this paper we study properties of regular solutions of quaternionic Riccati equations. The obtained results we use for study of the asymptotic behavior of solutions of two first-order linear quaternionic ordinary differential equations.
Remarks on semilinear problems with nonlinearities depending on the derivative.
Second-order -point eigenvalue problems on time scales.
Singular Dirichlet boundary value problems. II: Resonance case
Existence results are established for the resonant problem a.e. on with satisfying Dirichlet boundary conditions. The problem is singular since is a Carathéodory function, with a.e. on and .