A linear completely nonhomogeneous generally nonlocal multipoint problem is investigated for a fourth-order differential equation with generally nonsmooth coefficients satisfying some general conditions such as pintegrability and boundedness. A system of five integro-algebraic equations called an adjoint system is introduced for this problem. A concept of a Green functional is introduced as a s...

In this article, we study five non-homogeneous multi-point boundary-value problems (BVPs) of second order differential equations with the onedimensional p-Laplacian. These problems have a common equation (in different function domains) and different boundary conditions. We find conditions that guarantee the existence of at least three positive solutions. The results obtained generalize several ...

Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, nonhomogeneous wavelets and framelets enjoy many desirable theoretical properties and are often intrinsically linked to the refinable structure and multiresolution analysis. In this ...

It is shown that the nonhomogeneous Dirichlet and Neuman problems for the 2nd-order Seiberg-Witten equation on a compact 4-manifold X admit a regular solution once the nonhomogeneous Palais-Smale condition is satisfied. The approach consists in applying the elliptic techniques to the variational setting of the Seiberg-Witten equation. The gauge invariance of the functional allows to restrict th...

Two piecewise Hermite bicubic orthogonal spline collocation schemes are considered for the approximate solution of elliptic, self-adjoint, nonhomogeneous Dirichlet boundary value problems on rectangles. In the rst scheme, the nonhomogeneous Dirichlet boundary condition is approximated by means of the piecewise Hermite cubic interpolant, while the piecewise cubic interpolant at the boundary Gaus...

A laser-driven particle source is exploited for the elemental and stratigraphic characterization of a nonhomogeneous sample.

The fracture behaviors near the interface crack tip for mode II of orthotropic bimaterial are discussed. The oscillatory singularity fields are researched. The stress functions are chosen which contain twelve undetermined coefficients and an unknown singularity exponent. Based on the boundary conditions and linear independence, the system of twelve nonhomogeneous linear equations is derived. Ac...

We study a semiparametric pseudo-likelihood inference for nonhomogeneous Gamma process with random effects for degradation data. The setting for degradation data is one in which n independent subjects, each with a nonhomogeneous Gamma process, are observed at possible different times. The random effects are used to represent heterogeneity of degradation paths. To obtain the maximum pseudo-likel...