A general variational principle and some of its applications

By Biagio Ricceri. 2004

534 citations recorded by the source corpus.

Abstract In this paper, given a reflexive real Banach space X and two sequentially weakly lower semicontinuous functionals Φ,Ψ on X with Ψ strongly continuous and coercive, we are mainly interested in the existence of infinitely many local minima of the functional Φ+λΨ for each sufficiently large λ∈ R .

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/ff91cfcc89674e091180a9cdba2114a2e02c557f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Sublevel sets and global minima of coercive functionals and local minima of their perturbations (2004, methodology): “In [24], we have identified a general variational principle of which the following theorem is a by-product: THEOREM A.”
Lower semicontinuity of functionals of fractional type and applications to nonlocal equations with critical Sobolev exponent (2015, background): “1; part a)] (see also [28]), which assures the existence of a critical point (actually a minimum) for a functional, under suitable regularity assumptions on it.”
Three solutions for a nonlocal Dirichlet boundary value problem involving the p(x)-Laplacian (2013, methodology): “In 2002, Marano and Motreanu [38] extended Ricceri’s result to a large class of non-differentiable functionals and gave an application to a semilinear elliptic eigenvalue problem with highly discontinuous nonlinearities.”
Multiple solutions of p-biharmonic equations with Navier boundary conditions (2014, result): “The obtained results are related to some recent contributions from [10, Theorem 1] where, by using a critical point result from [16], the existence of at least three weak solutions has been obtained (see also [11, Theorem 1]).”
Existence results for one‐dimensional fractional equations (2014, methodology): “1, in the following, we will perform the variational principle of Ricceri established in [13].”
A three critical points theorem and its applications to the ordinary Dirichlet problem (2003, methodology): “Its proof is based on the variational principle of B.Ricceri ([ 16 ]) (see also [17]) and on the mountain pass theorem as expressed by P.Pucci and J.Serrin in [14].”
Arbitrarily small weak solutions for a nonlinear eigenvalue problem in Orlicz–Sobolev spaces (2012, result): “This result is a refinement of the Variational Principle of Ricceri, contained in [20].”
Quasilinear elliptic non-homogeneous Dirichlet problems through Orlicz-Sobolev spaces (2012, methodology): “The main tool in order to prove our multiplicity result is the following critical point theorem obtained in [27] that we recall here in a convenient form; see also the variational principle of Ricceri [28].”