Search results for "Solutions"
showing 10 items of 757 documents
Infinitely many solutions for a mixed boundary value problem
2010
The existence of infinitely many solutions for a mixed boundary value problem is established. The approach is based on variational methods.
Uniqueness of positive radial solutions to singular critical growth quasilinear elliptic equations
2015
In this paper, we prove that there exists at most one positive radial weak solution to the following quasilinear elliptic equation with singular critical growth \[ \begin{cases} -\Delta_{p}u-{\displaystyle \frac{\mu}{|x|^{p}}|u|^{p-2}u}{\displaystyle =\frac{|u|^{\frac{(N-s)p}{N-p}-2}u}{|x|^{s}}}+\lambda|u|^{p-2}u & \text{in }B,\\ u=0 & \text{on }\partial B, \end{cases} \] where $B$ is an open finite ball in $\mathbb{R}^{N}$ centered at the origin, $1<p<N$, $-\infty<\mu<((N-p)/p)^{p}$, $0\le s<p$ and $\lambda\in\mathbb{R}$. A related limiting problem is also considered.
Porphyrin-bile acid conjugates: from saccharide recognition in the solution to the selective cancer cell fluorescence detection.
2008
This paper describes the preparation and use of conjugates of porphyrins and bile acids as ligands to bind to tumor expressed saccharides. Bile acid-porphyrin conjugates were tested for recognition of saccharides that are typically present on malignant tumor cells. Fluorescence microscopy, in vitro PDT cell killing, and PDT of subcutaneous 4T1 mouse tumors is reported. High selectivity for saccharide cancer markers and cancer cells was observed. This in vivo and in vitro study demonstrated high potential use for these compounds in targeted photodynamic therapy.
GFP-mut2 Proteins in Trehalose-Water Matrixes: Spatially Heterogeneous Protein-Water-Sugar Structures
2007
We report investigations on the properties of nanoenvironments around single-GFP-mut2 proteins in trehalose-water matrixes. Single-GFPmut2 molecules embedded in thin trehalose-water films were characterized in terms of their fluorescence brightness, bleaching dynamics, excited state lifetime, and fluorescence polarization. For each property, sets of approximately 100-150 single molecules have been investigated as a function of trehalose content and hydration. Three distinct and interconverting families of proteins have been found which differ widely in terms of bleaching dynamics, brightness, and fluorescence polarization, whose relative populations sizably depend on sample hydration. The r…
La communication : en long, en large mais surtout en travers
2016
International audience; Dans le cycle de conférences autour de « la communication, un enjeu citoyen », ma démarche est sans doute particulière puisqu'elle vise tout particulièrement l'enseignement de la communication. Et pourtant, il nous semble que cet enseignement participe pleinement à la notion de citoyen responsable. Une communication sur la communication. Voilà ce que le titre évoque. Mais si le titre de ce texte fait place à la communication, il se veut équivoque. En effet, l'expression « en travers » prête à commentaire. Aussi, précisons que celle-ci désigne la transversalité de la discipline et de son enseignement. Communication ! Le mot à lui tout seul laisse rêveur, tant il est u…
Serrin-Type Overdetermined Problems: an Alternative Proof
2008
We prove the symmetry of solutions to overdetermined problems for a class of fully nonlinear equations, namely the Hessian equations. In the case of the Poisson equation, our proof is alternative to the proofs proposed by Serrin (moving planes) and by Weinberger. Moreover, our proof makes no direct use of the maximum principle while it sheds light on a relation between the Serrin problem and the isoperimetric inequality.
Planck scale physics and topology change through an exactly solvable model
2014
We consider the collapse of a charged radiation fluid in a Planck-suppressed quadratic extension of General Relativity (GR) formulated à la Palatini. We obtain exact analytical solutions that extend the charged Vaidya-type solution of GR, which allows to explore in detail new physics at the Planck scale. Starting from Minkowski space, we find that the collapsing fluid generates wormholes supported by the electric field. We discuss the relevance of our findings in relation to the quantum foam structure of space–time and the meaning of curvature divergences in this theory.
Quasi-rational solutions of the Hirota equation depending on multi-parameters and rogue waves
2023
Quasi-rational solutions to the Hirota equation are given. We construct explicit expressions of these solutions for the first orders. As a byproduct, we get quasi-rational solutions to the focusing NLS equation and also rational solutions to the mKdV equation. We study the patterns of these configurations in the (x, t) plane.
Generalized Camassa-Holm Equations: Symmetry, Conservation Laws and Regular Pulse and Front Solutions
2021
In this paper, we consider a member of an integrable family of generalized Camassa–Holm (GCH) equations. We make an analysis of the point Lie symmetries of these equations by using the Lie method of infinitesimals. We derive nonclassical symmetries and we find new symmetries via the nonclassical method, which cannot be obtained by Lie symmetry method. We employ the multiplier method to construct conservation laws for this family of GCH equations. Using the conservation laws of the underlying equation, double reduction is also constructed. Finally, we investigate traveling waves of the GCH equations. We derive convergent series solutions both for the homoclinic and heteroclinic orbits of the…
Cavity solitons in nondegenerate optical parametric oscillation
2000
Abstract We find analytically cavity solitons in nondegenerate optical parametric oscillators. These solitons are exact localised solutions of a pair of coupled parametrically driven Ginzburg–Landau equations describing the system for large pump detuning. We predict the existence of a Hopf bifurcation of the soliton resulting in a periodically pulsing localised structure. We give numerical evidence of the analytical results and address the problem of cavity soliton interaction.