Solutions Of Quasilinear Elliptic Equations Research Articles

Regularity for solutions of quasilinear elliptic equations under minimal assumptions

Regularity for solutions of quasilinear elliptic equations under minimal assumptions

Nonexistence and other properties for solutions of quasilinear elliptic equations

Nonexistence and other properties for solutions of quasilinear elliptic equations

A relation between critical values and eigenvalues in nonliner minimax problems

The paper establishes a relation between constrained minimax values of a functional g on a Hilbert space and related eigenvalues. If g is Frechet differentiable and weakly continuous, in presence of a saddle point geometry the minimax value σ(t) of g over corresponds to a set of eigenfunctions satisfying Moreover,γ has left and right hand derivatives and each of the is an eigenvalue. This abstract statement is written in mind of applications to existence of multiple nodal solutions for quasilinear elliptic equations.

Classification of positive solutions of quasilinear elliptic equations

Classification of positive solutions of quasilinear elliptic equations

Uniqueness of positive solutions for quasilinear elliptic equations when a parameter is large

Existence and uniqueness results are proved for positive solutions of a class of quasilinear elliptic equations in a domain Ω⊂ℝN via a generalisation of Serrin's sweeping principle. In the case when Ω is an annulus, it is shown that the solution is radially symmetric.

Conditions for the existence of a fundamental solution of quasilinear elliptic equations and higher-order systems with discontinuous coefficients

Conditions for the existence of a fundamental solution of quasilinear elliptic equations and higher-order systems with discontinuous coefficients

On the differentiability of solutions of quasilinear elliptic equations

On the differentiability of solutions of quasilinear elliptic equations

Explosive solutions of quasilinear elliptic equations: existence and uniqueness

Explosive solutions of quasilinear elliptic equations: existence and uniqueness

Positive Solutions of Quasilinear Elliptic Equations on Riemannian Manifolds

Positive Solutions of Quasilinear Elliptic Equations on Riemannian Manifolds

On the behavior of solutions of quasilinear elliptic equations of second order in unbounded domains

Analogues of the well known in the theory of analytic functions Phragmen-Lindeloff theorem are formulated for the solutions of a wide class of quasilinear equations of elliptic type. Examples are given which illustrate the sharpness of the obtained results for solutions of equations of the form div(|∇u|α−2∇u)=f(x, u), where the function f(x, u) is locally bounded in IRn+1,f(x, 0)=0,uf(x, u)⩾a¦u¦1+q,a>0,α>1,α-1>q⩾0, n>/2.

Uniqueness for viscosity solutions of quasilinear elliptic equations in ${\bf R}^N$ without conditions at infinity

By means of suitable interior estimates, uniqueness for continuous viscosity solutions of equations like -Δu+ H(∇u) + λum = f in RN are obtained, provided f ∈ C(RN), λ > m > 1 and H is uniformly continuous. Then the classical Perron method is used in proving the existence whenever H(O) ≤ f(middot;)in RN. © 1992, Khayyam Publishing. All rights reserved.

A priori estimate for maximum modulus of generalized solutions of quasi-linear elliptic equations

Let G be a bounded domain in E n .Consider the following quasi-linear elliptic equation Although the boundedness of generalized solutions of the equation is proved for very general structural conditions, it does not supply a priori estimate for maximum modulus of solutions. In this paper an estimate to the maximum modulus is made firstly for a special case of quasi-linear elliptic equations, i.e. the $$\overrightarrow A $$ and B satisfy the following structural conditions:

On the existence of radial solutions of quasilinear elliptic equations

The authors give a method for proving the existence of (positive) radial solutions of quasi-linear elliptic equations taking into account the variation of lower-order terms. They find solutions of equations having oscillating nonlinearities under less restrictive conditions than those needed for variational or topological methods. They exhibit simple variational problems having a continuum of solutions. They also obtain invariant regions in C1 for related parabolic problems.

Local Behavior of Solutions of Quasilinear Elliptic Equations With General Structure

Local Behavior of Solutions of Quasilinear Elliptic Equations With General Structure

Local behavior of solutions of quasilinear elliptic equations with general structure

This paper is motivated by the observation that solutions to certain variational inequalities involving partial differential operators of the form div ⁡ A ( x , u , ∇ u ) + B ( x , u , ∇ u ) \operatorname {div} A(x,u,\nabla u) + B(x,u,\nabla u) , where A A and B B are Borel measurable, are solutions to the equation div ⁡ A ( x , u , ∇ u ) + B ( x , u , ∇ u ) = μ \operatorname {div} A(x,u,\nabla u) + B(x,u,\nabla u) = \mu for some nonnegative Radon measure μ \mu . Among other things, it is shown that if u u is a Hölder continuous solution to this equation, then the measure μ \mu satisfies the growth property μ [ B ( x , r ) ] ⩽ M r n − p + ε \mu [B(x,r)] \leqslant M{r^{n - p + \varepsilon }} for all balls B ( x , r ) B(x,r) in R n {{\mathbf {R}}^n} . Here ε \varepsilon depends on the Hölder exponent of u u while p > 1 p > 1 is given by the structure of the differential operator. Conversely, if μ \mu is assumed to satisfy this growth condition, then it is shown that u u satisfies a Harnack-type inequality, thus proving that u u is locally bounded. Under the additional assumption that A A is strongly monotonic, it is shown that u u is Hölder continuous.

Multiple solutions for quasilinear elliptic equations

Multiple solutions for quasilinear elliptic equations

Local and global properties of solutions of quasilinear elliptic equations

We study the positive radial solutions of the equation div(¦Du¦ p − 2 Du) + u q = 0 for 0 < p − 1 < q . When q < Np (N − p) − 1 we give the complete classification of the isolated singularities of the above equation.

On positive solutions of quasi-linear elliptic equations

In this note we prove the existence of positive solutions of the Dirichlet problem for a quasi-linear elliptic equation. Our boundary data belongs to L2 and a corresponding solution is in a weighted Sobolev space.

A numerical method for solving quasilinear elliptic equations with a small parameter for the highest derivatives

A method for the numerical solution of quasilinear elliptic equations in which the coefficient of the highest derivatives is a small parameter is constructed. This method provides an error estimate which is uniform with respect to the parameter. A non-linear difference scheme is constructed on the basis of the method of straight lines and the use of exact difference schemes for one-dimensional problems. The computation grid is selected in such a way that the grid points crowd together in a special way near the boundary of the domain. An iterative algorithm, uniformly convergent with respect to the small parameter, is proposed for solving the non-linear scheme.

On bounded positive solutions of quasilinear elliptic equations in $R^n$

On considere l'existence des solutions entieres positives bornees des deux equations elliptiques quasi lineaires suivantes: div(Du(1+|Du| 2 ) −1/2 )=±Φ(|x|)u 9 dans R n , n≥3 ou q>1