Search results for "Differential operator"
showing 10 items of 70 documents
Supersymmetric structures for second order differential operators
2012
Necessary and sufficient conditions are obtained for a real semiclassical partial differential operator of order two to possess a supersymmetric structure. For the operator coming from a chain of oscillators, coupled to two heat baths, we show the non-existence of a smooth supersymmetric structure, for a suitable interaction potential, provided that the temperatures of the baths are different.
A? * algebra of pseudodifferential operators on noncompact manifolds
1988
On montre qu'une classe d'operateurs pseudodifferentiels d'ordre zero a la propriete d'invariance spectrale
Spectral invariance for algebras of pseudodifferential operators on besov-triebel-lizorkin spaces
1993
The algebra of pseudodifferential operators with symbols inS1,δ0, δ<1, is shown to be a spectrally invariant subalgebra of ℒ(bp,qs) and ℒ(Fp,qs).
Invariance spectrale des algèbres d'opérateurs pseudodifférentiels
2002
We construct and study several algebras of pseudodifferential operators that are closed under holomorphic functional calculus. This leads to a better understanding of the structure of inverses of elliptic pseudodifferential operators on certain non-compact manifolds. It also leads to decay properties for the solutions of these operators. To cite this article: R. Lauter et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 1095–1099.
Spectral Invariance and Submultiplicativity for the Algebras of S(M, g)-pseudo-differential Operators on Manifolds
2003
For appropriate triples (M, g, M), where M is an (in general non-compact) manifold, g is a metric on T*M, and M is a weight function on T* M, we developed in [5] a pseudo-differential calculus on.A.4 which is based on the S(M, g)-calculus of L. Hormander [30] in local models. Here we prove that the algebra of operators of order zero is a submultiplicative Ψ*-algebra in the sense of B. Gramsch [21] in \( \mathcal{L}\left( {{L^2}\left( M \right)} \right)\). For the basic calculus we generalized the concept of E. Schrohe [40] of so-called SG-compatible manifolds. In the proof of the existence of “order reducing operators” we apply a method from [4], and the proof of spectral invariance and sub…
Nonlinear nonhomogeneous Neumann eigenvalue problems
2015
We consider a nonlinear parametric Neumann problem driven by a nonhomogeneous differential operator with a reaction which is $(p-1)$-superlinear near $\pm\infty$ and exhibits concave terms near zero. We show that for all small values of the parameter, the problem has at least five solutions, four of constant sign and the fifth nodal. We also show the existence of extremal constant sign solutions.
Positive solutions for singular double phase problems
2021
Abstract We study the existence of positive solutions for a class of double phase Dirichlet equations which have the combined effects of a singular term and of a parametric superlinear term. The differential operator of the equation is the sum of a p-Laplacian and of a weighted q-Laplacian ( q p ) with discontinuous weight. Using the Nehari method, we show that for all small values of the parameter λ > 0 , the equation has at least two positive solutions.
Integrability of the one dimensional Schrödinger equation
2018
We present a definition of integrability for the one dimensional Schroedinger equation, which encompasses all known integrable systems, i.e. systems for which the spectrum can be explicitly computed. For this, we introduce the class of rigid functions, built as Liouvillian functions, but containing all solutions of rigid differential operators in the sense of Katz, and a notion of natural boundary conditions. We then make a complete classification of rational integrable potentials. Many new integrable cases are found, some of them physically interesting.
Nonlinear Nonhomogeneous Robin Problems with Almost Critical and Partially Concave Reaction
2020
We consider a nonlinear Robin problem driven by a nonhomogeneous differential operator, with reaction which exhibits the competition of two Caratheodory terms. One is parametric, $$(p-1)$$-sublinear with a partially concave nonlinearity near zero. The other is $$(p-1)$$-superlinear and has almost critical growth. Exploiting the special geometry of the problem, we prove a bifurcation-type result, describing the changes in the set of positive solutions as the parameter $$\lambda >0$$ varies.
On the Fučík spectrum of the p-Laplacian with no-flux boundary condition
2023
In this paper, we study the quasilinear elliptic problem \begin{align*} \begin{aligned} -\Delta_{p} u&= a\l(u^+\r)^{p-1}-b\l(u^-\r)^{p-1} \quad && \text{in } \Omega,\\ u & = \text{constant} &&\text{on } \partial\Omega,\\ 0&=\int_{\partial \Omega}\left|\nabla u\right|^{p-2}\nabla u\cdot \nu \,\diff \sigma,&& \end{aligned} \end{align*} where the operator is the $p$-Laplacian and the boundary condition is of type no-flux. In particular, we consider the Fu\v{c}\'{\i}k spectrum of the $p$-Laplacian with no-flux boundary condition which is defined as the set $\fucik$ of all pairs $(a,b)\in\R^2$ such that the problem above has a nontrivial solution. It turns out…