Search results for "Boundary value problem"

On the number of solutions of a Duffing equation

1991

The exact number of solutions of a Duffing equation with small forcing term and homogeneous Neumann boundary conditions is given. Several bifurcation diagrams are shown.

A class of shear deformable isotropic elastic plates with parametrically variable warping shapes

2017

A homogeneous shear deformable isotropic elastic plate model is addressed in which the normal transverse fibers are allowed to rotate and to warp in a physically consistent manner specified by a fixed value of a real non-negative warping parameter ω. On letting ω vary continuously (at fixed load and boundary conditions), a continuous family of shear deformable plates Pω is generated, which spans from the Kirchhoff plate at the lower limit ω=0, to the Mindlin plate at the upper limit ω=∞; for ω=2, Pω identifies with the third-order Reddy plate. The boundary-value problem for the generic plate Pω is addressed in the case of quasi-static loads, for which a principle of minimum total potential …

Fixed point theorems on ordered metric spaces and applications to nonlinear elastic beam equations

2012

In this paper, we establish certain fixed point theorems in metric spaces with a partial ordering. Presented theorems extend and generalize several existing results in the literature. As application, we use the fixed point theorems obtained in this paper to study existence and uniqueness of solutions for fourth-order two-point boundary value problems for elastic beam equations.

A boundary min-max principle as a tool for boundary element formulations

1991

Abstract A min-max principle for elastic solids, expressed in terms of the unknown boundary displacements and tractions, is presented. It is shown that its Euler-Lagrange equations coincide with the classical boundary integral equations for displacements and for tractions. This principle constitutes a suitable starting point for a symmetric sign-definite formulation of the boundary element method.

Multiplicity of solutions for two-point boundary value problems with asymptotically asymmetric nonlinearities

1996

Porous medium equation with absorption and a nonlinear boundary condition

2002

where is a bounded domain with smooth boundary, @=@ is the outer normal derivative, m ? 1; p; and q are positive parameters and u0 is in L∞( ). Problems of this form arise in mathematical models in a number of areas of science, for instance, in models for gas or :uid :ow in porous media [3] and for the spread of certain biological populations [13]. In the semilinear case (that is for m=1), there is an extensive literature about global existence and blow-up results for this type of problems, see among others, [5,9,16] and the literature therein. For the degenerate case (that is for m = 1), with a nonlinear boundary condition, local existence and uniqueness of weak solutions which are limit o…

Figures of equilibrium in close binary systems

1992

The equilibrium configurations of close binary systems are analyzed. The autogravitational, centrifugal and tidal potentials are expanded in Clairaut's coordinates. From the set of the total potential angular terms an integral equations system is derived. The reduction of them to ordinary differential equations and the determination of the boundary conditions allow a formulation of the problem in terms of a single variable.

A geometrical criterion for nonexistence of constant-sign solutions for some third-order two-point boundary value problems

2020

We give a simple geometrical criterion for the nonexistence of constant-sign solutions for a certain type of third-order two-point boundary value problem in terms of the behavior of nonlinearity in the equation. We also provide examples to illustrate the applicability of our results.

Gradient elasticity and nonstandard boundary conditions

2003

Abstract Gradient elasticity for a second gradient model is addressed within a suitable thermodynamic framework apt to account for nonlocality. The pertinent thermodynamic restrictions upon the gradient constitutive equations are derived, which are shown to include, besides the field (differential) stress–strain laws, a set of nonstandard boundary conditions. Consistently with the latter thermodynamic requirements, a surface layer with membrane stresses is envisioned in the strained body, which together with the above nonstandard boundary conditions make the body constitutively insulated (i.e. no long distance energy flows out of the boundary surface due to nonlocality). The total strain en…

Finite element approximation of parabolic hemivariational inequalities

1998

In this paper we introduce a finite element approximation for a parabolic hemivariational initial boundary value problem. We prove that the approximate problem is solvable and its solutions converge on subsequences to the solutions of the continuous problem