A discontinuous problem involving the -Laplacian operator and critical exponent in .
A discontinuous problem with quasilinear operator.
A double eigenvalue problem for Schrödinger equations involving sublinear nonlinearities at infinity.
A doubly degenerate elliptic system
A few results about the -Laplace's operator.
A few symmetry results for nonlinear elliptic PDE on noncompact manifolds
A finite-dimensional reduction method for slightly supercritical elliptic problems.
A finiteness theorem for the space of harmonic sections.
A free boundary problem for semilinear elliptic equations.
A free boundary problem for some modified predator-prey model in a higher dimensional environment
We focus on the free boundary problems for a Leslie-Gower predator-prey model with radial symmetry in a higher dimensional environment that is initially well populated by the prey. This free boundary problem is used to describe the spreading of a new introduced predator. We first establish that a spreading-vanishing dichotomy holds for this model. Namely, the predator either successfully spreads to the entire space as goes to infinity and survives in the new environment, or it fails to establish...
A game interpretation of the Neumann problem for fully nonlinear parabolic and elliptic equations
We provide a deterministic-control-based interpretation for a broad class of fully nonlinear parabolic and elliptic PDEs with continuous Neumann boundary conditions in a smooth domain. We construct families of two-person games depending on a small parameter ε which extend those proposed by Kohn and Serfaty [21]. These new games treat a Neumann boundary condition by introducing some specific rules near the boundary. We show that the value function converges, in the viscosity sense, to the solution...
A generalization of Aubry-Mather theory to partial differential equations and pseudo-differential equations
A geometric analysis of a singular ODE related to the study of a quasilinear PDE.
A geometric and analytic approach to some problems associated with Emden equations
A global approach to ground state solutions.
A global bifurcation result of a Neumann problem with indefinite weight.
A Global Compactness Result for Elliptic Boundary Value Problems Involving Limiting Nonlinearities.
A global differentiability result for solutions of nonlinear elliptic problems with controlled growths
Let be a bounded open subset of , . In we deduce the global differentiability result for the solutions of the Dirichlet problem with controlled growth and nonlinearity . The result was obtained by first extending the interior differentiability result near the boundary and then proving the global differentiability result making use of a covering procedure.
-harmonic equations and the Dirac operator.
A Hölder infinity Laplacian
In this paper we study the limit as p → ∞ of minimizers of the fractional Ws,p-norms. In particular, we prove that the limit satisfies a non-local and non-linear equation. We also prove the existence and uniqueness of solutions of the equation. Furthermore, we prove the existence of solutions in general for the corresponding inhomogeneous equation. By making strong use of the barriers in this construction, we obtain some regularity results.