Multiplicity and stability of closed geodesics on Finsler 2-spheres
A survey of recent progress on the multiplicity and stability problems for closed geodesics on Finsler 2-spheres is given.
Multiplicity of homoclinic orbits for a class of asymptotically periodic Hamiltonian systems
We prove the existence of infinitely many geometrically distinct homoclinic orbits for a class of asymptotically periodic second order Hamiltonian systems.
Multiplicity of positive and nodal solutions for nonhomogeneous elliptic problems in unbounded cylinder domains.
Multiplicity of positive solutions for second order quasilinear equations
We discuss the existence and multiplicity of positive solutions for a class of second order quasilinear equations. To obtain our results we will use the Ekeland variational principle and the Mountain Pass Theorem.
Multiplicity of positive solutions of nonlinear elliptic equations with critical sobolev exponent in some contractible domains.
Multiplicity of solutions for a class of elliptic systems in .
Multiplicity of solutions for gradient systems using Landesman-Lazer conditions.
Multiplicity results for nonlinear elliptic equations.
Multiplicity results for -sublinear -Laplacian problems involving indefinite eigenvalue problems via Morse theory.
Multiplicity results for the prescribed scalar curvature on low spheres
In this paper, we consider the problem of multiplicity of conformal metrics of prescribed scalar curvature on standard spheres . Under generic conditions we establish someMorse Inequalities at Infinity, which give a lower bound on the number of solutions to the above problem in terms of the total contribution of its critical points at Infinityto the difference of topology between the level sets of the associated Euler-Lagrange functional. As a by-product of our arguments we derive a new existence...
Multivalued harmonic morphisms.
Natural first order Lagrangians for immersions
We define natural first order Lagrangians for immersions of Riemannian manifolds and we prove a bijective correspondence between such Lagrangians and the symmetric functions on an open subset of m-dimensional Euclidean space.
Natural Lagrangian structures
Natural pseudodistances between closed surfaces
Let us consider two closed surfaces , of class and two functions , of class , called measuring functions. The natural pseudodistance between the pairs , is defined as the infimum of as varies in the set of all homeomorphisms from onto . In this paper we prove that the natural pseudodistance equals either , , or , where and are two suitable critical values of the measuring functions. This shows that a previous relation between the natural pseudodistance and critical values...
Neumann problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces
We study a nonlinear Neumann boundary value problem associated to a nonhomogeneous differential operator. Taking into account the competition between the nonlinearity and the bifurcation parameter, we establish sufficient conditions for the existence of nontrivial solutions in a related Orlicz–Sobolev space.
New examples of biharmonic maps in spheres
We give some new methods to construct nonharmonic biharmonic maps in the unit n-dimensional sphere 𝕊ⁿ.
New Examples of harmonic diffeomorphisms of the hyperbolic plane onto itself.
New results on the classical problem of Plateau on the existence of many solutions
New solutions of equations on
Newton and conjugate gradient for harmonic maps from the disc into the sphere
We compute numerically the minimizers of the Dirichlet energyamong maps from the unit disc into the unit sphere that satisfy a boundary condition and a degree condition. We use a Sobolev gradient algorithm for the minimization and we prove that its continuous version preserves the degree. For the discretization of the problem we use continuous finite elements. We propose an original mesh-refining strategy needed to preserve the degree with the discrete version of the algorithm (which is a preconditioned...