Custom sandwich pairs

AbstractFor many equations arising in practice, the solutions are critical points of functionals. In previous papers we have shown that there are pairs of subsets, called sandwich pairs, that can produce critical points even though they do not separate the functional. All that is required is that the functional be bounded from above on one of the sets and bounded from below on the other, with no relationship needed between the bounds. This provides a distinct advantage in applications. The present paper discusses the situation in which one cannot find sandwich pairs for which the functional is bounded below on one set and bounded above on the other. We develop a method which can deal with such situations and apply it to problems in partial differential equations

Sandwich pairs for p-Laplacian systems

AbstractWe solve boundary value problems for p-Laplacian systems using sandwich pairs

Rotationally invariant periodic solutions of semilinear wave equations

Under suitable conditions we are able to solve the semilinear wave equation in any dimension. We are also able to compute the essential spectrum of the linear wave operator for the rotationally invariant periodic case

Extended Black Box Theorem for Lepton Number and Flavor Violating processes

We revisit the well known "Black Box" theorem establishing a fundamental relation between the amplitude of neutrinoless double beta decay and the effective Majorana neutrino mass. We extend this theorem to the general case of arbitrary lepton number and lepton flavor violating (LFNV) processes and to the three generation Majorana neutrino mass matrix. We demonstrate the existence of a general set of one-to-one correspondence relations between the effective operators generating these processes, and elements of the neutrino mass matrix, such that if one of these two quantities vanishes the other is guaranteed to vanish as well, and moreover, if one of these quantities is non-zero the other is guaranteed to be non-zero. We stress that this statement remains valid even in the presence of arbitrary new physics contributions. As a particularly important example, we then show that neutrino oscillation data imply that neutrinoless double beta decay must occur at a certain non-zero rate.Comment: 11 pages, 1 fi

Sign-changing critical points via Sandwich Pair theorems

The Sandwich Pair theorems have presented very efficient ways to determine the existence of critical points or critical sequences for nonlinear differentiable functionals. In this paper, under rather weak hypotheses new relationships are established between sign-changing critical points and Sandwich Pairs or Linking Sandwich Pairs. The abstract results are demonstrated by applications on semi-linear elliptic equations. © 2013 Elsevier Ltd. All rights reserved

Finding linking sets

We present the most general definition of the linking of sets in a Banach space and discuss necessary and sufficient conditions for sets to link

Morse theory applied to semilinear problems

We use Morse theoretic arguments to obtain nontrivial solutions of semilinear elliptic boundary value problems where the nonlinearity interacts with the spectrum, without assuming that the asymptotic limits at zero and infinity exist