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Nonlinear elliptic equations involving the p-laplacian with mixed Dirichlet-Neumann boundary conditions

Bonanno Gabriele, D'Agui Giuseppina, Sciammetta Angela

Opuscula Mathematica

2019

Vol. 39, no. 2

159--174

In this paper, a nonlinear differential problem involving the p-Laplacian operator with mixed boundary conditions is investigated. In particular, the existence of three non-zero solutions is established by requiring suitable behavior on the nonlinearity. Concrete examples illustrate the abstract results.

Mixed problems for infinite systems of quasilinear hyperbolic functional differential equations

Kozieł S.

Demonstratio Mathematica

2003

Vol. 36, nr 3

659--674

The paper is concerned with initial-boundary problems for quasilinear infinite systems of first order partial differential functional equations. The unknown function is the functional variable in the system, the partial derivatives appear in a classical sense. A theorem on the existence and uniqueness of the Caratheodory solution and continuous dependence upon initial-boundary data is proved. The mixed problem is equivalent in a suitable function space to a system of functional integral equations. Infinite differential systems with a deviated argument and differential integral problems can be derived from a general model by specializing given functions.

Microlocal parametrices for a mixed problem with diffractive boundary

Kołakowski H.

Bulletin of the Polish Academy of Sciences. Mathematics

1999

Vol. 47, no 4

369-376

Following the works of M. Taylor and K. Kubota [3], [5] a parametrix for a three-dimensional mixed problem with diffractive boundary for the Lame equation is constructed. The two-dimensional case was investigated by Taylor [5]. If the wave front sets (WF(f)) of right-hand sides of the boundary conditions do not contain glancing points, this construction is almost the same as in [5] (see also [1]. In the case when W F( f ) contains diffractive points Kubota's method is used.