On certain nonlinear elliptic systems with indefinite terms
Electronic Journal of Differential Equations, 2002 We consider an elliptic quasi linear systems with indefinite term on a bounded domain. Under suitable conditions, existence and positivity results for solutions are given. Submitted April 2, 2002. Published October 2, 2002.
Ahmed Bensedik, Mohammed Bouchekif
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Existence of solutions for quasilinear elliptic systems involving critical exponents and Hardy terms
Electronic Journal of Differential Equations, 2013 Using variational methods, including the Ljusternik-Schnirelmann theory, we prove the existence of solutions for quasilinear elliptic systems with critical Sobolev exponents and Hardy terms.
Dengfeng Lu
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Infinitely many solutions for nonlocal elliptic systems of (p_1,...,p_n)-Kirchhoff type
Electronic Journal of Differential Equations, 2012 We establish the existence of infinitely many solutions for a class of nonlocal elliptic systems of (p_1,...,p_n)-Kirchhoff type. Our approach is based on variational methods.
Shapour Heidarkhani, Johnny Henderson
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Multi-dimensional Morse Index Theorems and a symplectic view of elliptic boundary value problems [PDF]
, 2011 Morse Index Theorems for elliptic boundary value problems in multi-dimensions are proved under various boundary conditions. The theorems work for star-shaped domains and are based on a new idea of measuring the "oscillation" of the trace of the set of ...
Deng, Jian +1 more
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Numerical analysis of a relaxed variational model of hysteresis in two-phase solids [PDF]
, 2001 This paper presents the numerical analysis for a variational formulation of rate-independent phase transformations in elastic solids due to Mielke et al.
Carstensen, Carsten +3 more
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Multiscale Geometric Integration of Deterministic and Stochastic Systems [PDF]
, 2011 In order to accelerate computations and improve long time accuracy of numerical simulations, this thesis develops multiscale geometric integrators. For general multiscale stiff ODEs, SDEs, and PDEs, FLow AVeraging integratORs (FLAVORs) have been ...
Tao, Molei
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Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps [PDF]
, 2013 Coarse spaces are instrumental in obtaining scalability for domain decomposition methods for partial differential equations (PDEs). However, it is known that most popular choices of coarse spaces perform rather weakly in the presence of heterogeneities ...
Hauret, P. +12 more
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An upper bound for validity limits of asymptotic analytical approaches based on normal form theory [PDF]
, 2012 Perturbation methods are routinely used in all fields of applied mathematics where analytical solutions for nonlinear dynamical systems are searched.
LAMARQUE, Claude-Henri +2 more
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Ground and bound state solutions for quasilinear elliptic systems including singular nonlinearities and indefinite potentials [PDF]
Communications on Pure and Applied Analysis, 2018 It is established existence of bound and ground state solutions for quasilinear elliptic systems driven by (\phi 1, \phi 2)-Laplacian operator. The main feature here is to consider quasilinear elliptic systems involving both nonsingular nonlinearities ...
Marcos L. M. Carvalho +3 more
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Compact embeddings of broken Sobolev spaces and applications [PDF]
, 2009 In this paper, we present several extensions of theoretical tools for the analysis of discontinuous Galerkin (DG) method beyond the linear case.
Buffa, Annalisa, Ortner, Christoph
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