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A general variational principle and some of its applications
TLDR
In this paper, the existence of infinitely many local minima of the functional capital Phi + r Psi for each sufficiently real r is studied. But the existence is not studied in this paper.Abstract:
In this paper, given a reflexive real Banach space X and two sequentially weakly lower semicontinuous functionals Phi, Psi on X with Psi strongly continuous and coercive, we are mainly interested in the existence of infinitely many local minima of the functional capital Phi + r Psi for each sufficiently real r.read more
Citations
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Infinitely many positive solutions for Kirchhoff-type problems
TL;DR: In this paper, Zhang et al. showed that the existence of infinitely many positive solutions to a class of Kirchhoff-type problems can be found in L ∞ ( Ω ), where Ω is a smooth bounded domain of R N, a, b > 0, λ > 0.
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Infinitely Many Solutions for a Boundary Value Problem with Discontinuous Nonlinearities
TL;DR: In this article, the existence of infinitely many solutions for a Sturm-Liouville boundary value problem, under an appropriate oscillating behavior of the possibly discontinuous nonlinear term, is obtained.
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Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities
TL;DR: In this paper, critical points theorems for non-differentiable functionals are established and applications both to elliptic variational-hemivariational inequalities and eigenvalue problems with discontinuous nonlinearities are presented.
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A critical point theorem via the Ekeland variational principle
TL;DR: In this article, the existence of a local minimum for a continuously Gâteaux differentiable function, possibly unbounded from below, without requiring any weak continuity assumption, is established and a novel definition of Palais-Smale condition is presented.
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Three solutions to a Neumann problem for elliptic equations involving the p-Laplacian
TL;DR: In this article, the existence of three solutions to a Neumann problem involving the p-Laplacian was established based on a three critical points theorem, and the technical approach was mainly based on the three-critical points theorem.
References
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Book
Minimax methods in critical point theory with applications to differential equations
TL;DR: The mountain pass theorem and its application in Hamiltonian systems can be found in this paper, where the saddle point theorem is extended to the case of symmetric functionals with symmetries and index theorems.
Journal ArticleDOI
Eigenvalues for semilinear boundary value problems
Martin Schechter,Kyril Tintarev +1 more
TL;DR: In this paper, the authors consider the problem of computing the values of the values for which (1.1) has a nontrivial solution u, assuming that g(u) is continuously Fr6chet differentiable and that g and u are both weakly continuous.
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