In the countably dimensional, separable and locally compact spaces, some class of admissible mappings was defined that is also closed due to composition and that has similar properties to the properties of single-valued mappings. A certain property of these maps was applied in the proof of Theorem 3.7, which is the main result of this work.
We study the existence of positive solutions of a system of higher-order nonlinear differential equations subject to multi-point boundary conditions, where the nonlinearities do not possess any sublinear or superlinear growth conditions and may be singular. In the proof of the main results, we use the Guo-Krasnosel'skii fixed point theorem.
Using variational methods, we estabilish existence of positive solutions for a class of quasilinear elliptic problems
where is a positive, continuous perturbations of a periodic function, H is the Heaviside function and f is a continuous function with subcritical growth. The results of the semilinear equations are extended to the quasilinear problem.
It was shown by Seeley that associated with a parameter-elliptic boundary problem involving a system of differential operators of homogeneous type there was associated an analytic semigroup. This result was extended by Dreher to a Douglis-Nirenberg system of mono-order type, i.e., the diagonal operators are all of the same order. In this paper we again discuss the problem considered by Dreher, but use a different approach as his approach gives rise to certain difficulties. We also extend the results for mono-order systems to a certain class of Douglis-Nirenberg systems of multiorder type, i.e., the diagonal operators are not all of the same order. 2010 Mathematics Subject Classification: 35J55; 47D06.
In this paper, we present a new iterative scheme for finding a common point among the set of solution of equilibrium problems, the set of solution to a variational inequality problem and the fixed point set of -strictly pseudo-contractive mappings in a real Hilbert space. We then prove that the proposed scheme converges strongly to a common element which is the solution of a variational inequality problem, system of equilibrium problems, and a fixed point of -strictly pseudo-contractive mappings. These results improve and generalize recent works in this direction.
McCoy  considered the approximation of pseudoanalytic functions (PAF) on the disk. Pseudoanalytic functions are constructed as complex combination of real - valued analytic solutions to the Stokes-Beltrami System. These solutions include the generalized biaxisymmetric potentials. McCoy obtained some coecient and Bernstein type growth theorems on the disk. The aim of this paper is to generalize the results of McCoy . Moreover, we study the generalized order and generalized type of PAF in terms of Fourier coecients occurring in its local expansion and optimal approximation errors in Bernstein sense on the disk. Our approach and method are dierent from those of McCoy .
In this paper, we consider an extended vector equilibrium problem and prove some existence results in the setting of Hausdorff topological vector spaces and reflexive Banach spaces. Our results extend and improve some known results in the literature. Some examples are given.
In this work we investigate the Neumann boundary value problem in the unit ball for a nonhomogeneous biharmonic equation. It is well known, that even for the Poisson equation this problem does not have a solution for an arbitrary smooth right hand side and boundary functions; it follows from the Green formula, that these given functions should satisfy a condition called the solvability condition. In the present paper these solvability conditions are found in an explicit form for the natural generalization of the Neumann problem for the non-homogeneous biharmonic equation. The method used is new for these type of problems. We first reduce this problem to the Dirichlet problem, then use the Green function of the Dirichlet problem recently found by T. Sh. Kal’menov and D. Suragan.
The fractional sub-equation method is proposed to construct analytical solutions of nonlinear fractional partial differential equations (FPDEs), involving Jumarie’s modified Riemann-Liouville derivative. The fractional sub-equation method is applied to the space-time fractional generalized Hirota-Satsuma coupled KdV equation and coupled mKdV equation. The analytical solutions show that the fractional sub-equation method is very effective for the fractional coupled KdV and mKdV equations. The solutions are compared with that of the extended tanh-function method. New exact solutions are found for the coupled mKdV equation.