Related papers: Existence results and numerical method of fourth o…
This paper deals with the Darcy-Forchheimer problem with two kinds of boundary conditions. We discretize the system by using the finite element methods and we propose two iterative schemes to solve the discrete problems. The well-posedness…
This paper deals with some classes of Kirchhoff type problems on a double phase setting and with nonlinear boundary conditions. Under general assumptions, we provide multiplicity results for such problems in the case when the perturbations…
The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…
In this paper, we present a new iterative approximate method of solving boundary value problems. The idea is to compute approximate polynomial solutions in the Bernstein form using least squares approximation combined with some properties…
In this paper, we investigate the existence of nontrivial weak solutions for the Prandtl-Batchelor type free boundary value elliptic problem driven by a power nonlinearity. The algebraic topology approach will be used to establish the…
The initial value problem is considered for a higher order nonlinear Schr\"odinger equation with quadratic nonlinearity. Results on existence and uniqueness of weak solutions are obtained. In the case of an effective at infinity additional…
Some superlinear fourth order elliptic equations are considered. Ground states are proved to exist and to concentrate at a point in the limit. The proof relies on variational methods, where the existence and concentration of nontrivial…
In this work we establish existence and multiplicity of solutions for elliptic problem with nonlinear boundary conditions under strong resonance conditions at infinity. The nonlinearity is resonance at infinity and the reso- nance phenomena…
We study a boundary-value quasilinear elliptic problem on a generic time scale. Making use of the fixed-point index theory, sufficient conditions are given to obtain existence, multiplicity, and infinite solvability of positive solutions.
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
This paper analyzes the structure of the set of nodal solutions of a class of one-dimensional superlinear indefinite boundary values problems with an indefinite weight functions in front of the spectral parameter. Quite astonishingly, the…
In this paper, we study existence results for initial value problems for hybrid fractional integro-differential equations. Our investigation is based on the Dhage hybrid fixed point theorem. Some fundamental fractional differential…
In this paper, we analyze nonlinear differential equations subject to generalized boundary conditions. More specifically, we provide a framework from which we can provide conditions, which are straightforward to check, for the solvability…
This article is concerned with the existence and uniqueness of solutions to some fractional order boundary value problems. Our results are based on some fixed point theorems. For the applicability of our results, we provide an example.
Existence and uniqueness of solutions for $\alpha\in\left( 2,3\right] $ order fractional differential equations with three point fractional boundary and integral conditions is discussed. The results are obtained by using standard fixed…
Recently, the nonlinearity continuation method has been used to numerically solve boundary value problems for steady-state Richards equation. The method can be considered as a predictor-corrector procedure with the simplest form which has…
In the present article we present a particular combination of boundary problems for the inhomogeneous tri-analytic equation: the Neumann-(Dirichlet-Neuman) problem and the (Dirichlet-Neumann)-Dirichlet problem. In order to obtain the…
In this work, we investigate the existence of positive solutions for a multi-point boundary value problem for a second order delay differential equation. Under certain growth conditions on the nonlinearity, and by the mean of Leray-Schauder…
Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori…
In this paper, we analyze an eigenvalue problem for nonlinear elliptic operators involving homogeneous Dirichlet boundary conditions in a open smooth bounded domain. We prove bifurcation results from trivial solutions and from infinity for…