Infinitely many solutions for a Robin boundary value problem.
Infinitely many solutions for a semilinear elliptic equation with sign-changing potential.
Infinitely many solutions for a semilinear elliptic equation in via a perturbation method
We introduce a method to treat a semilinear elliptic equation in (see equation (1) below). This method is of a perturbative nature. It permits us to skip the problem of lack of compactness of but requires an oscillatory behavior of the potential b.
Infinitely many solutions for an elliptic system with nonlinear boundary conditions.
Infinitely many solutions for asymptotically linear periodic Hamiltonian elliptic systems
This paper is concerned with the following periodic Hamiltonian elliptic system Assuming the potential V is periodic and 0 lies in a gap of , is periodic in x and asymptotically quadratic in , existence and multiplicity of solutions are obtained via variational approach.
Infinitely many solutions for Kirchhoff-type equations involving critical growth in Orlicz-Sobolev with negative energies
We investigate a class of Kirchhoff-type equations characterized by critical growth within Orlicz-Sobolev spaces. The main result establishes the existence of infinitely many solutions with negative energy. Using an adapted concentration-compactness principle and advanced variational methods, we overcome key challenges such as non-compactness and non-differentiability to the associated functionals. This work extends existing results to more general functional spaces, offering new insights into nonlocal...
Infinitely many solutions for the -Laplace equations with nonsymmetric perturbations.
Infinitely many solutions for the p(x)-Laplacian equations without (AR)-type growth condition
Under no Ambrosetti-Rabinowitz-type growth condition, we study the existence of infinitely many solutions of the p(x)-Laplacian equations by applying the variant fountain theorems due to Zou [Manuscripta Math. 104 (2001), 343-358].
Infinitely many solutions of strongly indefinite semilinear elliptic systems.
Infinitely many weak solutions for a non-homogeneous Neumann problem in Orlicz--Sobolev spaces
Under a suitable oscillatory behavior either at infinity or at zero of the nonlinear term, the existence of infinitely many weak solutions for a non-homogeneous Neumann problem, in an appropriate Orlicz--Sobolev setting, is proved. The technical approach is based on variational methods.
Infinitely many weak solutions for a -Laplacian equation with nonlinear boundary conditions.
Infinity Laplace equation with non-trivial right-hand side.
Influence of a boundary perforation on the Dirichlet energy
Inf-sup stable nonconforming finite elements of higher order on quadrilaterals and hexahedra
We present families of scalar nonconforming finite elements of arbitrary order with optimal approximation properties on quadrilaterals and hexahedra. Their vector-valued versions together with a discontinuous pressure approximation of order form inf-sup stable finite element pairs of order r for the Stokes problem. The well-known elements by Rannacher and Turek are recovered in the case r=1. A numerical comparison between conforming and nonconforming discretisations will be given. Since higher order...
Inheritance of symmetry for positive solutions of semilinear elliptic boundary value problems
Inhomogeneous boundary value problems for the von Kármán equations. II
Injections de Sobolev probabilistes et applications
On démontre dans cet article des versions probabilistes des injections de Sobolev sur une variété riemannienne compacte, . Plus précisément on démontre que pour des mesures de probabilité naturelles sur l’espace , presque toute fonction appartient à tous les espaces , . On donne ensuite des applications à l’étude des harmoniques sphériques sur la sphère : on démontre (encore pour des mesures de probabilité naturelles) que presque toute base hilbertienne de formée d’harmoniques sphériques...
Inner products in covolume and mimetic methods
A class of compatible spatial discretizations for solving partial differential equations is presented. A discrete exact sequence framework is developed to classify these methods which include the mimetic and the covolume methods as well as certain low-order finite element methods. This construction ensures discrete analogs of the differential operators that satisfy the identities and theorems of vector calculus, in particular a Helmholtz decomposition theorem for the discrete function spaces. This...
Innere Abschätzungen für Lösungen nichtlinearer elliptischer Differentialgleichungen zweiter Ordnung in n Variablen.
Instability of elliptic equations on compact Riemannian manifolds with non-negative Ricci curvature.