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Since the order of elliptic type model equation (Laplace equation) is two [1], [2], then it is natural the order of composite type model equation must be [3] [4] [5] three. At each point of the domain under consideration these equations have both real and complex characteristics. Notice that a boundary value problem for a composite type equation of second order first appeared in the paper [6]. The method for investigating the Fredholm property of boundary value problems is distinctive and belongs to one of the authors of the present paper.
A reaction-diffusion equation with power nonlinearity formulated either on the half-line or on the finite interval with nonzero boundary conditions is shown to be locally well-posed in the sense of Hadamard for data in Sobolev spaces. The result is e
This paper is concerned with the multiplicity results to a class of $p$-Kirchhoff type elliptic equation with the homogeneous Neumann boundary conditions by an abstract linking lemma due to Br{e}zis and Nirenberg. We obtain the twofold results in sub
In this paper we develop the global symbolic calculus of pseudo-differential operators generated by a boundary value problem for a given (not necessarily self-adjoint or elliptic) differential operator. For this, we also establish elements of a non-s
Many practical problems occur due to the boundary value problem. This paper evaluates the finite element solution of the boundary value problem of Poissons equation and proposes a novel a posteriori local error estimation based on the Hypercircle met
We study linear and quasilinear Venttsel boundary value problems involving elliptic operators with discontinuous coefficients. On the base of the a priori estimates obtained, maximal regularity and strong solvability in Sobolev spaces are proved.