On the palais-smale condition for nondifferentiable functionals
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In this article, two kinds of Palais-Smale conditions for nonsmooth functionals are studied, and it is shown that they are equivalent for convex functionals.Abstract:
Two kinds of Palais-Smale condition, $(PS)_c$ and $(PS)^*_c$, for nondifferentiable functionals are studied. It is shown that $(PS)_c$ implies $(PS)^*_c$ and that they are equivalent for convex functionals. This points out a gap in the proof of Costa and Goncalves [5, Proposition 3]. Some other nonsmooth versions of known smooth results are also obtained.read more
Citations
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Some Properties of General Minimization Problems with Constraints
Vy Khoi Le,Dumitru Motreanu +1 more
TL;DR: In this paper, the existence of solutions and necessary conditions of optimality for general minimization problems with constraints are studied and applications to an optimal control problem and a Lagrange multiplier rule are also given.
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Remarks on the infinite‐dimensional counterparts of the Darboux theorem
TL;DR: The Bolzano intermediate value theorem implies Darboux's theorem for continuous real-valued functions as discussed by the authors , which states that a continuous realvalued function defined on a compact interval has a zero value for at least one number −1.
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Existence Results for Quasilinear Elliptic Equations with Discontinuous Nonlinearities
TL;DR: In this paper, the nonsmooth critical point theory is applied to prove the existence of solutions and multiple solutions of a quasilinear elliptic equation with discontinuous nonlinearities.
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