The desire-satisfactionist defense of the existence of posthumous harm faces the problem of changing desires. The problem is that, in some cases where desires change before the time of their objects, the principle underlying the desire-satisfactionist defense of posthumous harm yields implausible results. In his prominent desire-satisfactionist defense of posthumous harm, David Boonin proposes a solution to this problem. First, I argue that there are two relevantly different versions of the problem of changing desires, and that Boonin's proposed solution addresses only one of them. Second, I argue that modifying the underlying principle is a better approach to overcoming the problem of changing desires since it addresses both versions of the problem. I defend this approach against objections by showing that the problems raised are problems for the principle as a general theory of harm, not for the principle as part of the desire-satisfactionist defense of posthumous harm.

This article is about nothing. Does that mean it is about something, namely, ‘nothing’? Or is there quite literally no thing that this article is about? Follow the dialogue between characters discussing the nature of non-existence and absences to find out! Along the way there will be tongue twisters, contradictions, paradoxes and riddles, ready to challenge our preconceptions of reality as we embark into the mysterious realm of nothingness.

Timothy Williamson has argued for the radical conclusion that everything necessarily exists. In this paper, I assume that the conclusion of Williamson's argument is more incredible than the denial of his premises. Under the assumption that Williamson is mistaken, I argue for the claim that there are some structured propositions which have constituents that might not have existed. If those constituents had not existed, then the propositions would have had an unfilled role; they would have been gappy. This gappy propositions view allows for a plausible response to Williamson's argument. Additionally, a slight variant of the gappy propositions view allows for plausible defense of Linguistic Ersatzism from the problem of contingent non-existents (also known as the problem of aliens).

In this paper, we investigate existence and non-existence of a nontrivial solution to the pseudo-relativistic nonlinear Schrödinger equation

$$\left( \sqrt{-c^2\Delta + m^2 c^4}-mc^2\right) u + \mu u = \vert u \vert^{p-1}u\quad {\rm in}~{\open R}^n~(n \ges 2) $$

In this paper, I propose a reading of Spinoza’s theory of the eternity of the mind in light of his theory of essence and existence. Opposing in particular recent Platonist readings of this theory, rejecting the dichotomy between formal essence and actual essence, upon which they mostly rely, I argue that Spinoza’s conception of the eternity of the mind must be grasped in terms of different aspects of one and the same existence. I moreover suggest that, for Spinoza, the mind was both sempiternal and eternal, without, however, those two aspects of the mind’s existence being identical.

This article studies propagating traveling waves in a class of reaction-diffusion systems which model isothermal autocatalytic chemical reactions as well as microbial growth and competition in a flow reactor. In the context of isothermal autocatalytic systems, two different cases will be studied. The first is autocatalytic chemical reaction of order m without decay. The second is chemical reaction of order m with a decay of order n, where m and n are positive integers and m>n≥1. A typical system in autocatalysis is A+2B→3B and B→C involving two chemical species, a reactant A and an auto-catalyst B and C an inert chemical species.

The numerical computation gives more accurate estimates on minimum speed of traveling waves for autocatalytic reaction without decay, providing useful insight in the study of stability of traveling waves.

For autocatalytic reaction of order m = 2 with linear decay n = 1, which has a particular important role in chemical waves, it is shown numerically that there exist multiple traveling waves with 1, 2 and 3 peaks with certain choices of parameters.

We are interested in entire solutions for the semilinear biharmonic equation Δ2 u = f(u) in ℝN , where f(u) = eu or –u –p (p > 0). For the exponential case, we prove that for the polyharmonic problem Δ2m u = eu with positive integer m, any classical entire solution verifies Δ2m–1 u < 0; this completes the results of Dupaigne et al. (Arch. Ration. Mech. Analysis208 (2013), 725–752) and Wei and Xu (Math. Annalen313 (1999), 207–228). We also obtain a refined asymptotic expansion of the radial separatrix solution to Δ2 u = eu in ℝ3, which answers a question posed by Berchio et al. (J. Diff. Eqns252 (2012), 2569–2616). For the negative power case, we show the non-existence of the classical entire solution for any 0 < p ⩽ 1.

We consider a class of even-order boundary-value problems with nonlinear boundary conditions and an eigenvalue parameter $\lambda$ in the equations. Sufficient conditions are obtained for the existence and non-existence of positive solutions of the problems for different values of $\lambda$.