An abstract theorem on the existence of hylomorphic solitons [PDF]
arXiv, 2011 In this paper we prove an abstract theorem which can be used to study the existence of solitons for various dynamical systems described by partial differential equations. We also give an idea of how the abstract theorem can be applied to prove the existence of solitons in some dynamical systems.
arxiv
Gauge Brezis-Browder Principles and Dependent Choice [PDF]
arXiv, 2013 The gauge Brezis-Browder Principle in Turinici [Bull. Acad. Pol. Sci. (Math.), 30 (1982), 161-166] is obtainable from the Principle of Dependent Choices (DC) and implies Ekeland's Variational Principle (EVP); hence, it is equivalent with both (DC) and (EVP).
arxiv
Three solutions for a fractional elliptic problems with critical and supercritical growth [PDF]
arXiv, 2014 In this paper, we deal with the existence and multiplicity of solutions for the fractional elliptic problems involving critical and supercritical Sobolev exponent via variational arguments. By means of the truncation combining with the Moser iteration, we prove that the problems has at least three solutions.
arxiv
Positive solutions to some asymptotically linear fractional Schrodinger equations [PDF]
arXiv, 2014 This paper is devoted to prove the existence and nonexistence of positive solutions for a class of fractional Schrodinger equation in RN of the We apply a new methods to obtain the existence of positive solutions when f(u) is asymptotically linear with respect to u at infinity.
arxiv
The quantitative Faber-Krahn inequality for the Robin Laplacian [PDF]
arXiv, 2016 We prove a quantitative Faber-Krahn inequality for the first eigenvalue of the Laplace operator with Robin boundary conditions. The asymmetry term involves the square power of the Fraenkel asymmetry, multiplied by a constant depending on the Robin parameter, the dimension of the space and the measure of the set.
arxiv
Anisotropic Isoperimetric Inequalities involving Boundary Momentum, Perimeter and Volume [PDF]
arXiv, 2018 We consider a scale invariant functional involving the anisotropic $p-$momentum, the anisotropic perimeter and the volume. We show that the Wulff shape, associated with the Finsler norm $F$ considered and centered at the origin, is the unique minimizer of the anisotropic functional taken into consideration among all bounded convex sets.
arxiv
Multiple positive solutions to a fourth order boundary value problem [PDF]
arXiv, 2015 We study the existence and multiplicity of positive solutions for a nonlinear fourth-order two-point boundary value problem. The approach is based on critical point theorems in conical shells, Krasnoselskii's compression-expansion theorem, and unilateral Harnack type inequalities.
arxiv
On the Morse Index of Critical Points in the Viscosity Method [PDF]
arXiv, 2018 We show that in viscous approximations of functionals defined on Finsler manifolds, it is possible to construct suitable sequences of critical points of these approximations satisfying the expected Morse index bounds as in Lazer-Solimini's theory, together with the entropy condition of Michael Struwe.
arxiv
A second order smooth variational principle on Riemannian manifolds [PDF]
arXiv, 2007 We establish a second order smooth variational principle valid for functions defined on (possibly infinite-dimensional) Riemannian manifolds which are uniformly locally convex and have a strictly positive injectivity radius and bounded sectional curvature.
arxiv
Some Remarks on the Fucik Spectrum of the p-Laplacian and Critical Groups [PDF]
arXiv, 2000 We compute critical groups of variational functionals arising from quasilinear elliptic boundary value problems with jumping nonlinearities, when the asymptotic limits of the equation lie in various regions of the plane that are separated by certain curves of the Fucik spectrum.
arxiv