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The second order of accuracy stable difference scheme for the numerical solution of the mixed problem for the fractional parabolic equation are presented using by r-modified Crank-Nicholson difference scheme. Sta...
This paper investigates the higher order differential equations with nonlocal boundary conditions
The fourth order matching operator on the hexagonal grid is constructed. Its application to the interpolation problem of the numerical solution obtained by hexagonal grid approximation of Laplace’s equation on...
In this paper we continue our research from (Monteiro and Tvrdý in Discrete Contin. Dyn. Syst. 33(1):283-303, 2013) on continuous dependence on a parameter k of solutions to linear integral equations of the form
In this work we consider the energy decay result and nonexistence of global solution for a reaction-diffusion equation with generalized Lewis function and nonlinear exponential growth. There are very few works...
In this paper, we discuss the expression and properties of Green’s function for boundary value problems of nonlinear Sturm-Liouville-type fractional order impulsive differential equations. Its applications are...
We study oscillatory properties of a class of second-order nonlinear neutral functional differential equations with distributed deviating arguments. On the basis of less restrictive assumptions imposed on the ...
In this note, we study a new class of ordinary differential equations with non-instantaneous impulses. Both existence and generalized Ulam-Hyers-Rassias stability results are established. Finally, an example i...
We discuss univalent solutions of boundary fractional differential equations in a complex domain. The fractional operators are taken in the sense of the Srivastava-Owa calculus in the unit disk. The existence ...
This paper deals with the resonance problem for the one-dimensional p-Laplacian with homogeneous Dirichlet boundary conditions and with nonlinear impulses in the derivative of the solution at prescribed points. T...
In this paper, we consider the following system of nonlinear third-order nonlocal boundary value problems (BVPs for short):
We study the existence and multiplicity of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations, subject to integral boundary conditions. The nonsingular and singula...
Consider the singular Dirichlet problem
In this article, the homotopy analysis method (HAM) is applied to solve the fractional cable equation by the Riemann-Liouville fractional partial derivative. This method includes an auxiliary parameter h which pr...
We obtain the asymptotic formulas for the eigenvalues and eigenfunctions of the Sturm-Liouville operators with some regular boundary conditions. Using these formulas, we find sufficient conditions on the poten...
We study oscillatory behavior of a class of fourth-order neutral differential equations with a p-Laplacian like operator using the Riccati transformation and integral averaging technique. A Kamenev-type oscillati...
The coefficients and delays in models describing various processes are usually obtained as a results of measurements and can be obtained only approximately. We deal with the question of how to estimate the inf...
This paper is devoted to the study of existence and dependence of solutions of the first-order periodic boundary value problems involving the distributional Henstock-Kurzweil integral. The methods used are mai...
A constructive technique for the study of boundary value problems for n th order differential equations with deviating arguments is described. A computer-assisted proof of the correct solvability of the considere...
New effective conditions are found for the validity of a theorem on differential inequalities corresponding to the Darboux problem for linear hyperbolic differential equations with argument deviations.
In the present paper we apply a sinc-Gaussian technique to compute approximate values of the eigenvalues of discontinuous Dirac systems, which contain an eigenvalue parameter in one boundary condition, with tr...
The original article was published in Boundary Value Problems 2013 2013:98
We study the existence of bounded oscillatory solutions for a higher order differential equation, considered as a perturbation of an associated linear equation. Jointly with this, we study the nonexistence of ...
This paper addresses the study of the controllability for a one-dimensional wave equation in domains with moving boundary. This equation characterizes the motion of a string with a fixed endpoint and the other...
Based on the integral representations of the solution derived via Fokas’ transform method, the high-frequency asymptotics for the solution of the modified Helmholtz equation, in a half-plane and subject to the...
In this paper, we establish the existence and multiplicity of symmetric positive solutions for a class of p-Laplacian fourth-order differential equations with integral boundary conditions. Our proofs use the Lera...
In this paper, the boundary value problem for the differential-operator equation with principal variable coefficients is studied. Several conditions for the separability and regularity in abstract
The Erratum to this article has been published in Boundary Value Problems 2014 2014:116
We investigate the extinction properties of non-negative nontrivial weak solutions of the initial-boundary value problem for a p-Laplacian evolution equation with nonlinear gradient source and absorption terms.
In this paper, using the theory of fixed point index on a cone and the Leray-Schauder fixed point theorem, we present the multiplicity of positive solutions for the singular nonlocal boundary-value problems in...
In this article, the author discusses the existence of solutions for a class of impulsive differential equations by means of a variational approach different from earlier approaches.
By generalizing the extension of the continuous theorem of Ge and Ren and constructing suitable Banach spaces and operators, we investigate the existence of solutions for p-Laplacian boundary value problems at re...
In this paper, we study periodic BVPs for fractional order impulsive evolution equations. The existence and boundedness of piecewise continuous mild solutions and design parameter drift for periodic motion of ...
In this paper, we deal with the existence of three nontrivial solutions for the potential system of p-Laplacian equations with homogeneous Dirichlet boundary conditions. Applying the Nehari procedure and abstract...
This work is concerned with the global existence and nonexistence of solutions for a quasilinear parabolic equation with null Dirichlet boundary condition. Based on the Galerkin approximation technique and the...
In this paper, we prove that the global existence of solutions to timelike minimal surface equations having arbitrary co-dimension with slow decay initial data in two space dimensions and three space dimension...
This paper considers the Cauchy problem of solutions for a class of sixth order 1-D nonlinear wave equations at high initial energy level. By introducing a new stable set we derive the result that certain solu...
We consider the nonlinear biharmonic equation with variable coefficient and polynomial growth nonlinearity and Dirichlet boundary condition. We get two theorems. One theorem says that there exists at least one...
We are concerned with the following nonlinear problem
In this paper, a new existence result is obtained for a fractional multivalued problem with fractional integral boundary conditions by applying a (Krasnoselskii type) fixed-point result for multivalued maps du...
In this article, the authors apply the super-solution and sub-solution methods, instead of energy estimate methods, to investigate the critical extinction exponents for a fast diffusion equation with a nonloca...
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