Solutions to a nonlinear drift-diffusion model for semiconductors.
Solutions to a perturbed critical semilinear equation concerning the -Laplacian in
The aim of this paper is to study the existence of variational solutions to a nonhomogeneous elliptic equation involving the -Laplacian where , is a bounded smooth domain in , , is a critical nonlinearity in the sense of the Trudinger-Moser inequality and is a small perturbation.
Solutions to -systems by topological and iterative methods.
Solutions to nonlinear elliptic equations with a nonlocal boundary condition.
Solutions to perturbed eigenvalue problems of the -Laplacian in .
Solutions to stationary phase-field equations.
Solutions to the mean curvature equation by fixed point methods.
Solvability for semilinear PDE with multiple characteristics
We prove local solvability in Gevrey spaces for a class of semilinear partial differential equations. The linear part admits characteristics of multiplicity k ≥ 2 and data are fixed in , 1 < σ < k/(k-1). The nonlinearity, containing derivatives of lower order, is assumed of class with respect to all variables.
Solvability of nonlinear Dirichlet problem for a class of degenerate elliptic equations.
Solvability of quasilinear elliptic equations with strong dependence on the gradient.
Solvability of semilinear equations with strong nonlinearities and applications to elliptic boundary value problems
Solving -Laplacian equations on complete manifolds.
Some approximation properties in Orlicz-Sobolev spaces
Some asymptotic error estimates for finite element approximation of minimal surfaces
Some asymptotic problems in fully nonlinear elliptic equations and stochastic control
Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations
We consider three types of semilinear second order PDEs on a cylindrical domain , where is a bounded domain in , . Among these, two are evolution problems of parabolic and hyperbolic types, in which the unbounded direction of is reserved for time , the third type is an elliptic equation with a singled out unbounded variable . We discuss the asymptotic behavior, as , of solutions which are defined and bounded on .
Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations
Some constancy results for harmonic maps from non-contractable domains into spheres.
Some constancy results for nematic liquid crystals and harmonic maps