This thematic series originates from the International Conference on the Theory, Methods and Applications of Nonlinear Equations which was held in December 2012 in Kingsville, TX-USA and was organized by the Department of Mathematics at the Texas A&M University-Kingsville.
Edited by: Ravi Agarwal, Shusen Ding, Billur Kaymakcalan, Dumitru Motreanu and Anthony To Ming Lau
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In this paper, we propose a new model for segmentation of both gray-scale and color images. This model is inspired by the GAC model, the region-scalable fitting model, the weighted bounded variation model and ...
In this paper we give a new refinement of discrete Jensen’s inequality, which generalizes a former result. The introduced sequences depend on parameters. The strict monotonicity and the convergence are investi...
The purpose of this paper is to establish some coupled coincidence point theorems for generalized nonlinear contraction mappings with the mixed g-monotone property in the framework of metric spaces endowed with p...
The paper deals with the existence and non-existence of solutions of the following strongly nonlinear non-autonomous boundary value problem:
We obtain several oscillation criteria for a class of second-order nonlinear neutral differential equations. New theorems extend a number of related results reported in the literature and can be used in cases ...
In this paper, we study the following singular semipositone boundary value problem on time scales:
We investigate multiple solutions for the Hamiltonian system with singular potential nonlinearity and periodic condition. We get a theorem which shows the existence of the nontrivial weak periodic solution for...
We study oscillation and asymptotic behavior of a class of third-order half-linear functional dynamic equations with an unbounded neutral coefficient. Several comparison theorems are presented that are essenti...
In this paper, we develop a multi-model adaptive control strategy to be applied on delay compensation schemes for stable/unstable LTI MIMO systems. The only requirement is that the delay should be bounded and ...
In this paper, we apply Picard operator theory to investigate a class of fractional differential equations with iterations of linear modification of the argument. For that, two useful work spaces
In this article we establish relative oscillation theorems for two discrete matrix Sturm-Liouville eigenvalue problems with Dirichlet boundary conditions and nonlinear dependence on the spectral parameter λ. This...
Of concern is the existence of mild solutions to delay fractional differential equations with almost sectorial operators. Combining the techniques of operator semigroup, noncompact measures and fixed point the...
We study oscillatory behavior of a class of second-order differential equations with damping under the assumptions that allow applications to retarded and advanced differential equations. New theorems extend a...
A Newton-Kantorovich convergence theorem of a new modified Halley’s method family is established in a Banach space to solve nonlinear operator equations. We also present the main results to reveal the competen...
By constructing suitable operators, we investigate the existence of solutions for a coupled system of fractional differential equations with integral boundary conditions at resonance. Our analysis relies on th...
In this paper, we consider a Lagrange-Galerkin scheme to approximate a two-dimensional fluid-structure interaction problem. The equations of the system are the Navier-Stokes equations in the fluid part, couple...
By establishing a comparison result and using the method of upper and lower solutions and the monotone iterative technique, we investigate the differential systems with coupled integral boundary value problems...
The existence of the nontrivial periodic solutions for nonautonomous second-order delay differential equation
In this paper, let X be a uniformly convex Banach space which either is uniformly smooth or has a weakly continuous duality map. We introduce and consider three-step Mann iterations for finding a common solution ...
In this paper, we investigate fixed point problems of a continuous pseudo-contraction based on a viscosity iterative scheme. Strong convergence theorems are established in a reflexive Banach space which also e...
In this paper, we establish the global Poincaré-type inequalities for the composition of the sharp maximal operator and Green’s operator with Orlicz norm.
In this paper, a class of second-order nonlinear perturbed differential equation and its special cases are studied. By using the generalized Riccati transformation and well-known techniques, some new oscillati...
In this article, fixed point problems of a family of strictly pseudocontractive mappings are investigated based on a viscosity iterative process. Strong convergence theorems are established in a real q-uniformly ...
Convergence of a new iterative scheme, containing Mann and Ishikawa iterative schemes, for asymptotically nonexpansive mappings on a 2-uniformly convex hyperbolic space is studied. As application, we find a so...
This work develops Feynman-Kac formulae for switching diffusion processes. It first recalls the basic notion of a switching diffusion. Then the desired stochastic representations are obtained for boundary valu...
The purpose of this paper is to present an iterative method for finding a common element of the set of solutions for an equilibrium problem and the set of common fixed points for a countably infinite family of...
We show that the fixed point methods allow to investigate Ulam’s type stability of additivity quite efficiently and precisely. Using them we generalize, extend and complement some earlier classical results con...
In this paper, we establish a strong convergence theorem for hierarchical problems, an equivalent relation between a multiple sets split feasibility problem and a fixed point problem. As applications of our re...
In this paper we utilize the notion of Ω-distance in the sense of Saadati et al. (Math. Comput. Model. 52:797-801, 2010) to construct and prove some fixed and coupled fixed point theorems in a complete G-metric s...
Very recently, Haghi et al. (Topol. Appl. 160:450-454, 2013) proved that some fixed point theorems in partial metric spaces can be obtained from metric spaces. In this paper, we prove some common fixed point theo...
We derive interior and global Hölder estimates for solutions of a class of quasilinear elliptic equations. First, the interior Hölder continuity is obtained by the iteration of an oscillation estimate. Then, t...
We first introduce a new concept of b-dislocated metric space as a generalization of dislocated metric space and analyze different properties of such spaces. A fundamental result for the convergence of sequences ...
Very recently, some authors discovered that some fixed point results in thecontext of a G-metric space can be derived from the fixed point resultsin the context of a quasi-metric space and hence the usual metric ...
Very recently, Samet et al. and Jleli and Samet reported that most of fixed point results in the context of G-metric space, defined by Sims and Zead, can be derived from the usual fixed point theorems on the usua...
In this paper, we introduce the concept of generalized convex contractions and give some results about approximate fixed points of the contractions on metric spaces. By providing some examples, we show that ou...
In this paper, we introduce composite Mann iteration methods for a general system of variational inequalities with solutions being also common fixed points of a countable family of nonexpansive mappings and ze...
Wardowski (Fixed Point Theory Appl. 2012:94, 2012, doi:10.1186/1687-1812-2012-94) introduced a new type of contraction called F-contraction and proved a fixed point result in complete metric spaces, which in turn...
This paper addresses the stabilization problem of the nonlinear Kirchhoff string using nonlinear boundary control. Nonlinear boundary control is the negative feedback of the transverse velocity of the string a...
This paper considers a kind of degenerate parabolic systems. First, we consider the initial boundary value problem of the two-species degenerate parabolic cooperative system. By using the method of a parabolic...
By applying an iterative technique, a necessary and sufficient condition is obtained for the existence of the unique solution of nonlinear fractional differential equations involving two Riemann-Liouville deri...
We study the following elliptic equations with variable exponents
In this paper the inverse problem of finding the time-dependent coefficient of heat capacity together with the nonlocal boundary conditions is considered. Under some natural regularity and consistency conditio...
Generalized asymptotically quasi-Ï•-nonexpansive mappings and a Ky Fan inequality are investigated. A strong convergence theorem for common solutions to a fixed point problem of generalized asymptotically quasi-Ï•-...