Saddle Points and Multiple Solutions of Differential Equations.
Scalar curvature, covering spaces, and Seiberg-Witten theory.
Second order conditions for extrema of functionals defined on regular surfaces.
Second order information on Palais-smale sequences in the mountain pass theorem.
Second variational derivative of local variational problems and conservation laws
We consider cohomology defined by a system of local Lagrangian and investigate under which conditions the variational Lie derivative of associated local currents is a system of conserved currents. The answer to such a question involves Jacobi equations for the local system. Furthermore, we recall that it was shown by Krupka et al. that the invariance of a closed Helmholtz form of a dynamical form is equivalent with local variationality of the Lie derivative of the dynamical form; we remark that...
Self-intersection Points in classical area-minimizing surfaces.
Semilinear elliptic equations having asymptotic limits at zero and infinity.
Shapes of spheres of special nonholonomic left-invariant intrinsic metrics on some Lie groups.
Sine - Laplace Equation, Sinh-Laplace Equation and Harmonic Maps.
Singly periodic solutions of a semilinear equation
Singularities of optimal averaged profit for stationary strategies.
Small eigenvalues of the Neumann realization of the semiclassical Witten Laplacian
This article follows the previous works [HeKlNi, HeNi] by Helffer-Klein-Nier and Helffer-Nier about the metastability in reversible diffusion processes via a Witten complex approach. Again, exponentially small eigenvalues of some self-adjoint realization of are considered as the small parameter tends to . The function is assumed to be a Morse function on some bounded domain with boundary . Neumann type boundary conditions are considered. With these boundary conditions, some possible simplifications...
Solution Brances of a semilinear elliptic problem at corak-2 Bifurcation points.
Solution of problem l (Vol. l (1953), p. 171) - 3 (Vol.1(1953),p172)
Solution of Signorini's contact problem in the deformation theory of plasticity by secant modules method
A problem of unilateral contact between an elasto-plastic body and a rigid frictionless foundation is solved within the range of the so called deformation theory of plasticity. The weak solution is defined by means of a variational inequality. Then the so called secant module (Kačanov's) iterative method is introduced, each step of which corresponds to a Signorini's problem of elastoplastics. The convergence of the method is proved on an abstract level.
Solution of the inverse problem of the calculus of variations
Given a family of curves constituting the general solution of a system of ordinary differential equations, the natural question occurs whether the family is identical with the totality of all extremals of an appropriate variational problem. Assuming the regularity of the latter problem, effective approaches are available but they fail in the non-regular case. However, a rather unusual variant of the calculus of variations based on infinitely prolonged differential equations and systematic use of...
Solution to a semilinear problem on type II regions determined by the Fučik spectrum.
Solutions of elliptic equations with indefinite nonlinearities via Morse theory and linking
Solutions of Minimal Period for a Class of Convex Hamiltonian Systems.
Solutions périodiques de systèmes hamiltoniens