Applicable Analysis: An International Journal

Dancer, E.N.; Yihong, DU

doi: 10.1080/00036819508840321pmid: N/A

In this paper we study the existence of sign-changing solutions of the problem -δu=f(u), u|∂D=0. In particular we answer some of the questions left open in an earlier paper by the authors.

Wiandt, Tamas

doi: 10.1080/00036819508840322pmid: N/A

The equation is considered. It was conjectured [I] that the condition is necessary for the global asymptotic stability of the zero solution. By the use of the Poincard-Bendixson theorem and the LaSalle invariance principle, a counterexample is given to this conjecture.

Holm, Hinrich; Stephan, Ernst P.

doi: 10.1080/00036819508840323pmid: N/A

Time-harmonic electromagnetic waves are scattered by a homogeneous dielectric obstacle. We transform Maxwell's equations via an ansatz into a system of second kind integral equations on the interface. Uniqueness and Fredholm properties of the boundary integral operator are proven. A Garding inequality is satisfied and ensures the stability of the corresponding Galerkin scheme.

Agarwal, Ravi P.; Pang, Petr Y. H.

doi: 10.1080/00036819508840324pmid: N/A

In this paper we present sharp Opial-type inequalities in two independent variables involving higher order partial derivatives. From the particular cases of our results we then correct as well as improve several recent inequalities.

Hines, Gwendolen

doi: 10.1080/00036819508840325pmid: N/A

In this paper we investigate upper semicontinuity of attractors for delay equations where the delay depends on a parameter. We are especially interested in delay equations with continuous memory functions. We interpret the results of Hines[l2] in this context, giving conditions on the memory functions under which we have upper semicontinuity. We then present some examples from the literature where we use these results to prove that attractors are upper semicontinuous.

Carl, S.; Dietrich, H.

doi: 10.1080/00036819508840326pmid: N/A

A variational approach to the method of upper and lower solution is suggested which allows to treat nonlinear elliptic boundary value problems with Baire-measurable lower order nonlinearities. To this end an associated multivalued setting of the problem is considered. First we prove the existence of solutions of a ‘truncated’ auxiliary problem which is related to the minimization of a nonsmooth functional whose critical points are shown to be solutions of this auxiliary problem. Then it is shown that any solution of the auxiliary problem solves the original one. The existence of critical points of the functional under consideration is proved by showing that it satisfies a generalized Palais-Smale condition which is suggested by the Variational Principle of Ekeland.

Badii, Muricio; Ildefonso Diaz, Jesus

doi: 10.1080/00036819508840327pmid: N/A

We prove the existence and uniqueness of periodic solutions of the equation ut = φ(u)xx + b(u)x with Dirichlet and N~umann boundary periodic data. The equation arises, for instance, in the mathematical modelling of the flow of groundwater in a homogeneous isotropic unsaturated porous medium. Those kinds of boundary data represent different periodic behaviours on the top and bottom of the medium due, for instance, to the seasons in the course of the years. The equation arises in many other contexts. We improve precedent results in the literature limited to the non degenerate case ( φ'(0) > 0) and uniformly bounded convection terms.

Miettinen, Markku

doi: 10.1080/00036819508840328pmid: N/A

We prove the existence of a solution of a constrained hemivariational inequality, and, develop a fully discrete approximation of it. The relation between the constrained hemivariational inequality and a problem of finding substationary points of the corresponding potential function is also studied.

Bartusšek, Miroslav; Došlá, Zuzana

doi: 10.1080/00036819508840329pmid: N/A

We study the existence of proper Kneser solutiolis of a systenl of differential equations. Especially, we remark how this result can be applied on a nonlinear differential equation with quasi-derivatives.

Tersian, Stefan

doi: 10.1080/00036819508840330pmid: N/A

The existence of nontrivial solutions u of the Schrödinger equation is proved under appropriate assumptions on V and f. It is also considered radially symmetric solutions of (S). Next an existence of nontrivial solutions u of the equation is considered, where is the first positive eigenvalue of the Laplacian in 0 with Dirichlet boundary conditions. The existence of axially symmetric solutions is also proved. The proofs of results are based on Mountain Pass Theorem and compact embeding lemmata.