Fu/v cik Spectrum for the Neumann Problem with Indefinite Weights [PDF]
arXiv, 2000 We obtain a description of the Fu\v{c}ik spectrum associated to the one-dimensional asymmetric problem with indefinite weights $Lu = am(t)u^+ - bn(t)u^-$ in $]T_1, T_2[$, $u'(T_1) = 0 = u'(T_2)$, where $L$ is a Sturm-Liouville operator. Our approach is based on the shooting method.
arxiv
On a nonlinear fourth order elliptic equation involving the Sobolev critical exponent [PDF]
arXiv, 2001 In this paper we use an algebraic topological argument due to Bahri and Coron to show how the topology of the domain influences the existence of positive solutions of some fourth order elliptic equation involving the critical Sobolev exponent.
arxiv
Existence results for an elliptic DirichletI problem
Le Matematiche, 2011 The main purpose of this paper is to present recent existence results for an elliptic eigenvalue Dirichlet problem. Precisely, our method ensures the existence of an exactly determined open interval (possibly unbounded) of positive parameters for which ...
Giuseppina D'Aguì +1 more
doaj
Compact embeddings and indefinite semilinear elliptic problems [PDF]
arXiv, 2002 Our purpose is to find positive solutions $u \in D^{1,2}(\rz^N)$ of the semilinear elliptic problem $-\laplace u = h(x) u^{p-1}$ for $2
arxiv
A stability result for nonlinear Neumann problems under boundary variations [PDF]
arXiv, 2002 In this paper we study, in dimension two, the stability of the solutions of some nonlinear elliptic equations with Neumann boundary conditions, under perturbations of the domains in the Hausdorff complementary topology.
arxiv
Multi-valued boundary value problems involving Leray-Lions operators and discontinuous nonlinearities [PDF]
arXiv, 2003 We prove an existence result for a class of Dirichlet boundary value problems with discontinuous nonlinearity and involving a Leray-Lions operator. The proof combines monotonicity methods for elliptic problems, variational inequality techniques and basic tools related to monotone operators.
arxiv
Optical design of two-reflector systems, the Monge-Kantorovich mass transfer problem and Fermat's principle [PDF]
arXiv, 2003 It is shown that the problem of designing a two-reflector system transforming a plane wave front with given intensity into an output plane front with prescribed output intensity can be formulated and solved as the Monge-Kantorovich mass transfer problem.
arxiv
Some remarks on sub-elliptic equations [PDF]
arXiv, 2003 In this paper, we consider the principal eigenvalue problem for Hormander's laplacian on $R^n$. We also study a related semi-linear sub-elliptic equation in the whole $R^n$ and prove that under a suitable condition, we have infinite many positive solutions of the problem.
arxiv
On a Paneitz Type Equation in Six Dimensional Domains [PDF]
arXiv, 2003 In this paper we consider a fourth order equation involving the critical Sobolev exponent on a bounded and smooth domain in $\R^6$. Using theory of critical points at infinity, we give some topological conditions on a given function defined on a domain to ensure some existence results.
arxiv
On the regularity of the polar factorization for time dependent maps [PDF]
arXiv, 2003 We consider the polar factorization of vector valued mappings introduced by Y. Brenier. In the case of a family of mappings depending on a parameter. We investigate the regularity with respect to this parameter of the terms of the polar factorization by constructing some a priori bounds.
arxiv