The development of new type hydrogels featuring enhanced properties is a recent topic and particular interest for wide range industrial applications, especially in biomedical sector. present contribution focuses on the mutliscale modeling that are treated by enzymatic mineralization thus enriched with calcium phosphate. More specifically, phosphate forms spherical or honeycomb structures hydrog...

In this work, we are interested in a boundary value problem (BVP) generated by Klein -Gordon equation (KG) with Jump conditions and condition. First, introduce scattering solutions Jost solution of the problem. Then, give function prove some properties it. Lastly, conclude paper special example.

We aim here at analyzing self-adjoint boundary value problems on finite networks associated with positive semi-definite Schrödinger operators. In addition, we study the existence and uniqueness of solutions and its variational formulation. Moreover, we will tackle a well-known problem in the framework of Potential Theory, the so-called condenser principle. Then, we generalize of the concept of ...

where (pn) and (qn), n ∈ Z are real sequences, and λ is an eigenparameter. We find a polynomial type Jost solution of this BVP. Then we investigate the analytical properties and asymptotic behavior of the Jost solution. Using the Weyl compact perturbation theorem, we prove that a self-adjoint discrete Dirac system has a continuous spectrum filling the segment [–2, 2]. We also prove that the Dir...

where a, b, A,B ∈ R, n ≥ 2 is an integer and f is a continuous, scalar-valued function. In recent years there have been many papers devoted to the solvability of twopoint boundary value problems for second-order or higher-order difference equations. We refer the reader to the textbooks [1,2,3], the papers [6,7] and the references therein. In [4] the following discrete boundary value problem (BV...

and Applied Analysis 3 In BVP 1.4 – 1.6 , it can be found that the boundary condition 1.5 is dependent on all the x a , x b , x′ a , and x′ b terms. First, existence and uniqueness of solutions of BVP 1.4 – 1.6 is established by combining the method of upper and lower solutions with LeraySchauder degree theory. Then, the general quasilinearization method is applied to construct the approximatio...

Estimations of the number of solutions are given for various resonant cases of the boundary value problem x′′ + g(t, x) = f(t, x, x′), x(a) cos α − x′(a) sin α = 0, x(b) cos β − x′(b) sin β = 0, where g(t, x) is an asymptotically linear nonlinearity, and f is a sublinear one. We assume that there exists at least one solution to the BVP. 2000 Mathematics Subject Classification: 34B15.

In this paper, we develop a general framework for studying Dirichlet Boundary Value Problems (BVP) for second order symmetric implicit differential systems satisfying the Hartman-Nagumo conditions, as well as a certain non-expandability condition. The main result, obtained by means of the equivariant degree theory, establishes the existence of multiple solutions together with a complete descrip...