This paper is concerned with a 2nth-order p-Laplacian difference equation. By using the critical point method, we establish various sets of sufficient conditions for the nonexistence and existence of solutions for Neumann boundary value problem and give some new results. Results obtained successfully generalize and complement the existing ones.

Laplace’s equation with mixed boundary conditions, that is, Dirichlet conditions on parts of the boundary and Neumann conditions on the remaining contiguous parts, is solved on an interior planar domain using an integral equation method. Rapid execution and high accuracy is obtained by combining equations which are of Fredholm’s second kind with compact operators on almost the entire boundary w...

In this article, we study a Kirchhoff type problem with nonlinear Neumann boundary conditions on a bounded domain. By using variational methods, we prove the existence of infinitely many solutions.

In this paper, we consider an acoustic wave transmission problem with mixed boundary conditions of Dirichlet, Neumann, and impedance type. We will derive a formulation as direct, space-time retarded integral equation, where both Cauchy data are kept unknowns on the part boundary. This requires definition single-trace spaces which incorporate homogeneous Dirichlet Neumann corresponding parts pro...

In this note self-adjoint realizations of second order elliptic differential expressions with non-local Robin boundary conditions on a domain Ω ⊂ Rn with smooth compact boundary are studied. A Schatten–von Neumann type estimate for the singular values of the difference of the mth powers of the resolvents of two Robin realizations is obtained, and for m > n 2 − 1 it is shown that the resolvent p...

this paper is concerned with a 2nth-order p-laplacian difference equation. by using the critical point method, we establish various sets of sufficient conditions for the nonexistence and existence of solutions for neumann boundary value problem and give some new results. results obtained successfully generalize and complement the existing ones.

A gauge-averaging functional of the axial type is studied for simple supergravity at one loop about flat Euclidean four-space bounded by a three-sphere, or two concentric three-spheres. This is a generalization of recent work on the axial gauge in quantum supergravity on manifolds with boundary. Ghost modes obey nonlocal boundary conditions of the spectral type, in that half of them obey Dirich...

Implicit a posteriori error estimators are developed for elliptic boundary value problems. Local problems are formulated for the error and the corresponding Neumann type boundary conditions are approximated using a new family of gradient averaging procedure. The convergence properties of the implicit error estimator are discussed independently from that of the residual type error estimators, wh...

Implicit a posteriori error estimators are developed for elliptic boundary value problems. Local problems are formulated for the error and the corresponding Neumann type boundary conditions are approximated using a new family of gradient averaging procedure. The convergence properties of the implicit error estimator are discussed independently from that of the residual type error estimators, wh...

The existence of trapped modes near obstacles in two-dimensional waveguides is well established when the centre-line of the guide is a line of symmetry for the geometry. In this paper we examine cases where no such line of symmetry exists. The boundary condition on the obstacle is of Neumann type and both Neumann and Dirichlet conditions on the guide walls are treated. A variety of techniques (...