Ce travail a pour objet d'évaluer l'apport de la physique quantique à la compréhension du phénomène de la conscience. Les modèles « classiques » de la conscience proposés actuellement laissent en suspens deux questions importantes: (a) l'explication de la synchronisation de régions éloignées du cerveau qui semble nécessaire à la construction de percepts conscients ; (b) la question du fossé explicatif qui existe entre l'expérience subjective, relevant de ce que le sujet est capable de ressentir de façon privée, et la description de ses corrélats neurophysiologiques dans le langage de la science, à la troisième personne. Les approches quantiques de la conscience sont systématiquement exposées et critiquées. Le « modèle dissipatif du cerveau »proposé par Vitiello et Freeman semble corroborer les données expérimentales et pourrait ainsi contribuer à résoudre cette dernière question (a). Ce modèle utilise une propriété fondamentale de la théorie quantique des champs selon laquelle la brisure spontanée de symétrie au sein d'un système physique donne lieu à l'émergence d'une dynamique collective pour ce système. Les modèles, relavant de la conception du monismeneutre, qui ont développés par Bohm et Hiley, et, plus récemment, par Atmanspacher et Primas, utilisent la théorie quantique pour son pouvoir expressif (concepts de complémentarité et d'intrication) et non comme une théorie de la seule matière pour bâtir une représentation unificatrice du phénomène de la conscience. Ils permettent de dissoudre la question (b) du fossé explicatif. Nous proposons enfin de prolonger et d'appliquer,plus généralement, ce mode de représentation au domaine psychosomatique. / This work aims to assess the contribution of quantum physics to the understanding of the phenomenon ofconsciousness. The "classical" models of consciousness cannat deal with two important questions: (a) thesynchronisation of distant parts of the brain which seems necessary to the construction of conscious percepts;(b) the question of the explanatory gap that exists between subjective experience, which is a private feeling, andthe description of its neurophysiological correlates in the language of science, at the third persan. The quantumalternatives of current models of consciousness are systematically exposed. Vitiello's and Freeman's "dissipativemadel of the brain" seem to corroborate experimental data and could thus contribute to solve question (a). Thismadel appeals to a fundamental property of quantum field theory according to which a spontaneous symmetrybreaking in a physical system (as it happens, the breaking of the rotational symmetry of dipolar molecules of thebrain) gives rise to a collective dynamics for this system. The models, relevant to the neutra! monism conception,that have been developed by Bohm and Hiley and, more recently, by Atmanspacher and by Primas use quantumtheory for its expressive power (concepts of complementarity and entanglement) to build a unifyingrepresentation of the phenomenon of consciousness. They lead to the dissolution of the question (b) of theexplanatory gap. ln the end, we suggest to extend this mode of representation and to apply it, more generally, tothe psychosomatic domain.

The thesis presents the results of our research on symmetry for some semilinear elliptic problems and on existence of solution for quasilinear problems involving singularities. The text is composed of two parts, each of which begins with a specific introduction. The first part is devoted to symmetry and symmetry-breaking results. We study a class of partial differential equations involving radial weights on balls, annuli or $R^N$ --where these weights are unbounded--. We show in particular that on unbounded domains, focusing on symmetric functions permits to recover compactness, which implies existence of solutions. Then, we stress the fact that symmetry-breaking occurs on bounded domains, depending both on the weights and on the nonlinearity of the equation. We also show that for the considered class of problems, the multibumps-solution phenomenon appears on the annulus as well as on the ball. The second part of the thesis is devoted to partial and ordinary differential equations with singularities. Using concentration-compactness tools, we show that a rather large class of functionals is lower semi-continuous, leading to the existence of a ground state solution. We also focus on the unicity of solutions for such a class of problems.