Existence of multiple positive solutions for fourth order two-point boundary value problems

The present article tackles two-point boundary value problems for fourth-order differential equations as follows <artwork name="GAPA31044eu1"> Several existence theorems on multiple positive solutions to the problems are obtained, and some examples are given to show the validity of these results.     

Existence and Multiplicity Results for the Nonlinear Klein-Gordon Equation

In this work, we study the multiplicity of solutions for a stationary nonhomogeneous problem associated to the nonlinear one-dimensional Klein-Gordon Equation. We prove that the existence of positive solutions is equivalent to the solvability of a scalar equation 2F(M) = 1, where F is a real function depending on V. Moreover, we prove some existence and multiplicity results for the Dirichlet problem in the superlinear case.     

Noninvariant Boundary Conditions

It is generally believed that in order to solve initial and boundary value problems using Lie symmetry methods, the boundary and initial conditions need to be left invariant by the infinitesimal symmetry generator which admits the invariant solution. In this article we give less restrictive conditions on the imposed initial and boundary values in order that they be recoverable with a particular symmetry generator.     

On a variational approach to some non-local boundary value problems

We treat by variational methods some nonlinear elliptic b.v.p. that involve a non-local term. Our main tools are the Mountain Pass Theorem of Ambrosetti and Rabinowitz and minimization procedures.     

Problems of Periodic Solutions for a Kind of Second Order Neutral Functional Differential Equation

By means of continuation theorem of coincidence degree theory, existence, nonexistence and unique existence criteria are established for the periodic solution of a kind of second order neutral functional differential equation.     

Boundedness of Solutions of Dirichlet Problem for a Class of Nonlinear Elliptic Equations with Weights

In this article, under some Hypotheses on weights and on coefficients, using a modification of Moser's method, we establish the boundedness of solutions of Dirichlet Problem for a class of nonlinear elliptic equations.     

Computational Results for Seamount Imaging in a Water Waveguide

This article presents our computational results for imaging a seamount in a waveguide. We assume that there is no knowledge of what kind of boundary condition on the unknown seamount. The incident waves are sent from point sources along a straight line and the corresponding scattered fields are measured from a line above the unknown seamount. Analysis and numerical results are presented.     

Maximizing Algebraic Connectivity Over Unicyclic Graphs

We consider the class of unicyclic graphs on n vertices with girth g, and over that class, we attempt to determine which graph maximizes the algebraic connectivity. When g is fixed, we show that there is an N such that for each n>N, the maximizing graph consists of a g cycle with n?g pendant vertices adjacent to a common vertex on the cycle. We also provide a bound on N. On the other hand, when g is large relative to n, we show that this graph does not maximize the algebraic connectivity, and we give a partial discussion of the nature of the maximizing graph in that situation.     

Multiplicity of homoclinics for a class of time recurrent second order Hamiltonian systems

We prove the existence of infinitely many homoclinic solutions for a class of second order Hamiltonian systems in of the form , where we assume the existence of a sequence such that and as for any . Moreover, under a suitable non degeneracy condition, we prove that this class of systems admits multibump solutions. Received February 2, 1996 / In revised form July 5, 1996 / Accepted October 10, 1996     

Fixed point theorems for multivalued operators and application to discontinuous quasilinear BVP's

In this article, we prove an abstract fixed point theorem for increasing multivalued operators in ordered topological spaces, which provides an efficient tool to obtain qualitative results on the solution set of discontinuous quasilinear elliptic boundary value problems. In particular, we are able to show the existence of extremal solutions of such problems.     

Convergence of a strong variational algorithm for relaxed controls involving a distributed optimal control problem of parabolic type 1

In this paper, we consider a class of Optimal Control problems involving first boundary value problems of parabolic type. A strong variational algorithm has been obtained for solving this class of optimal control problems in a paper by the author and D. W. Reid. It was also shown that any L∞ accumulation points of control sequences generated by the algorithm satisfy a necessary condition for optimality. Since such accumulation points need not exist, it is shown in this paper that control sequences generated by the algorithm always have accumulation points in the sense of control measure, and these accumulation points satisfy a necessary condition for optimality for the corresponding relaxed control problem.     

Convergence of a relaxation scheme for hyperbolic systems of conservation laws

Summary. This paper concerns the study of a relaxation scheme for hyperbolic systems of conservation laws. In particular, with the compensated compactness techniques, we prove a rigorous result of convergence of the approximate solutions toward an entropy solution of the equilibrium system, as the relaxation time and the mesh size tend to zero. Received September 29, 1998 / Revised version received December 20, 1999 / Published online August 24, 2000     

An index theory for paths that are solutions of a class of strongly indefinite variational problems

We generalize the Morse index theorem of [12,15] and we apply the new result to obtain lower estimates on the number of geodesics joining two fixed non conjugate points in certain classes of semi-Riemannian manifolds. More specifically, we consider semi-Riemannian manifolds admitting a smooth distribution spanned by commuting Killing vector fields and containing a maximal negative distribution for . In particular we obtain Morse relations for stationary semi-Riemannian manifolds (see [7]) and for the G?del-type manifolds (see [3]). Received: 4 April 2001 / Accepted: 27 September 2001 / Published online: 23 May 2002 The authors are partially sponsored by CNPq (Brazil) Proc. N. 301410/95 and N. 300254/01-6. Parts of this work were done during the visit of the two authors to the IMPA, Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil, in January and February 2001. The authors wish to express their gratitude to all Faculty and Staff of the IMPA for their kind hospitality.     

p-Laplacian Systems on Resonance

We assume certain (adapted to the case of a system) Landesman–Lazer-type conditions, in order to prove existence results for a p-Laplacian system on resonance.     

A Kato-Yau inequality and decay estimate for eigenspinors

We show that harmonic spinors obey a strengthened version of the well-known pointwise Kato inequality for sections of a vector bundle with a connection. We then give two different proofs an interesting decay estimate for harmonic spinors, one using our Kato-Yau estimate and resulting differential inequality, and a second using known eigenvalue calculations for the Dirac operator on the three-sphere. As an example of the use of these estimates, we also describe some new applications to the problems of gluing and ungluing PU(2) monopoles.     

Boundary limit theorems for positive hyperharmonic functions

We prove the following result: Let u be a positive hyperharmonic function on the open unit ball B?R ⁿ whose almost all radial limits are equal to zero and there are no such radial limits along which u tends to infinity. Then u is identically equal to zero.     

Three-scale asymptotics for a diffusion problem coupled with the wave equation

In this article, we present an asymptotic analysis of waves of elastic stress in an infinite solid whose boundary is subject to a rapid thermal load. The problem under consideration couples the wave equation and the heat equation, and the asymptotic approximation of the solution requires three-scaled variables. The asymptotic approximation is supplied with a rigorous remainder estimate and is illustrated numerically.     

Inverse Problems of Boundary Value Problems for Annular Vibrating Membranes with Piecewise Smooth Positive Functions in the Boundary Conditions

The asymptotic expansions of the trace of the heat kernel for small positive t, where λ_ν are the eigenvalues of the negative Laplacian in Rⁿ (n=2 or 3), are studied for a general annular bounded domain Ω with a smooth inner boundary ?Ω₁ and a smooth outer boundary ?Ω₂ where a finite number of piecewise smooth Dirichlet, Neumann and Robin boundary conditions on the components Γ _j (j=1,…,m) of ?Ω₁ and on the components of ?Ω₂ are considered such that and and where the coefficients in the Robin boundary conditions are piecewise smooth positive functions. Some applications of Θ (t) for an ideal gas enclosed in the general annular bounded domain Ω are given.