Solutions of problems in nonhomogeneous elasticity

Distributional Solutions of Nonhomogeneous

Discrete and continuous refinement equations have been widely studied in the literature for the last few years, due to their applications to the areas of wavelet analysis and geometric modeling. However, there is no “universal” theorem that deals with the problem about the existence of compactly supported distributional solutions for both discrete and continuous refinement equations simultaneou...

Local analytic solutions to some nonhomogeneous problems with p-Laplacian

Applying the Briot-Bouquet theorem we show that there exists an unique analytic solution to the equation ( tΦp (y ′) ) ′ +(−1)tΦq(y) = 0, on (0, a), where Φr(y) := |y| r−1 y, 0 < r, p, q ∈ R, i = 0, 1, 1 ≤ n ∈ N, a is a small positive real number. The initial conditions to be added to the equation are y(0) = A 6= 0, y′(0) = 0, for any real number A. We present a method how the solution can be e...

ON MAXWELL'S STRESS FUNCTIONS FOR SOLVING THREE DIMENSIONAL ELASTICITY PROBLEMS IN THE THEORY OF ELASTICITY

The governing equations of three dimensional elasticity problems include the six Beltrami-Michell stress compatibility equations, the three differential equations of equilibrium, and the six material constitutive relations; and these are usually solved subject to the boundary conditions. The system of fifteen differential equations is usually difficult to solve, and simplified methods are usual...

Multiplicity of Positive and Nodal Solutions for Nonhomogeneous Elliptic Problems in Unbounded Cylinder Domains

Interfering Solutions of a Nonhomogeneous Hamiltonian System

A Hamiltonian system is studied which has a term approaching a constant at an exponential rate at infinity . A minimax argument is used to show that the equation has a positive homoclinic solution. The proof employs the interaction between translated solutions of the corresponding homogeneous equation. What distinguishes this result from its few predecessors is that the equation has a nonhomoge...