Non-convex self-dual Lagrangians: New variational principles of symmetric boundary value problems
Abbas Moameni,Abbas Moameni +1 more
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TLDR
The Nc-SD Lagrangians as mentioned in this paper are a family of non-convex self-dual (NC-SD) Lagrangian functions and their derived vector fields which are associated to many partial differential equations and evolution systems.About:
This article is published in Journal of Functional Analysis.The article was published on 2011-05-01 and is currently open access. It has received 17 citations till now. The article focuses on the topics: Boundary value problem & Nonlinear system.read more
Citations
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A new variational principle, convexity, and supercritical Neumann problems
Craig Cowan,Abbas Moameni +1 more
TL;DR: Using a new variational principle that allows us to deal with problems beyond the usual locally compact structure, problems with a supercritical nonlinearity of the type
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Positive weak solutions of a generalized supercritical Neumann problem
F. Safari,Abdolrahman Razani +1 more
TL;DR: In this article, it was shown that a supercritical Neumann problem has at least one positive radial solution via variational principle and defining an energy functional with a hidden symmetry associated with the problem.
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Multiplicity results for elliptic problems with super-critical concave and convex nonlinearties
TL;DR: In this article, a multiplicity result for semilinear elliptic problems with a super-critical nonlinearity of the form, 1 − ε, ε ≥ 0.
Journal ArticleDOI
Critical point theory on convex subsets with applications in differential equations and analysis
TL;DR: In this article, a comprehensive variational principle that allows one to apply critical point theory on closed proper subsets of a given Banach space and yet, to obtain critical points with respect to the whole space is established.
Journal ArticleDOI
A variational principle for problems with a hint of convexity
TL;DR: In this paper, a variational principle is introduced to provide a new formulation and resolution for several boundary value problems with variational structure, which allows one to deal with problems well beyond the weakly compact structure.
References
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Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
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Elliptic Partial Differential Equations of Second Order
David Gilbarg,Neil S. Trudinger +1 more
TL;DR: In this article, Leray-Schauder and Harnack this article considered the Dirichlet Problem for Poisson's Equation and showed that it is a special case of Divergence Form Operators.
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Elliptic Partial Differential Equations of Second Order
Piero Bassanini,Alan R. Elcrat +1 more
TL;DR: In this paper, a class of partial differential equations that generalize and are represented by Laplace's equation was studied. And the authors used the notation D i u, D ij u for partial derivatives with respect to x i and x i, x j and the summation convention on repeated indices.
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Non-homogeneous boundary value problems and applications
TL;DR: In this paper, the authors consider the problem of finding solutions to elliptic boundary value problems in Spaces of Analytic Functions and of Class Mk Generalizations in the case of distributions and Ultra-Distributions.
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Convex analysis and variational problems
Ivar Ekeland,Roger Téman +1 more
TL;DR: In this article, the authors consider non-convex variational problems with a priori estimate in convex programming and show that they can be solved by the minimax theorem.