Uniqueness of entire solutions to quasilinear equations of $ p $-Laplace type

Entire Large Solutions of Quasilinear Elliptic Equations of Mixed Type

In this paper, the existence and nonexistence of nonnegative entire large solutions for the quasilinear elliptic equation   2 | | = ( ) ( ) ( ) ( ) m div u u p x f u q x g u     are established, where 2 m  , f and g are nondecreasing and vanish at the origin. The locally H older continuous functions p and q are nonnegative. We extend results previously obtained for special cases of f a...

STABILITY OF POSITIVE SOLUTIONS TO p&2–LAPLACE TYPE EQUATIONS

In this article, we first show the existence of a positive solution to { −Δpu−αΔu = λ(u− f (u)) in Ω, u = 0 on ∂Ω, by the method of lower and upper solutions and then under certain conditions on f , we show the stability of positive solution. Mathematics subject classification (2010): 35J92, 35B35, 35B05.

Entire Bounded Solutions for a Class of Quasilinear Elliptic Equations

Existence and Uniqueness of Solutions of Quasilinear Wave Equations (ii)

In this work we prove a result concernig the existence and uniqueness of solutions of quasilinear wave equation and we consider also their trivial solutions. We consider the following initial-boundary value problem for the nonlinear wave equation in the form u+ f (u) + g (u̇) = 0 in [0, T ) × Ω (QL) with initial values u0 = u (0, ·) , u1 = u̇ (0, ·) and boundary vale null, that is, u (t, x) = 0 o...

ENTIRE SOLUTIONS FOR A CLASS OF p-LAPLACE EQUATIONS IN R

We study the entire solutions of the p-Laplace equation − div(|∇u|p−2∇u) + a(x, y)W ′(u(x, y)) = 0, (x, y) ∈ R where a(x, y) is a periodic in x and y, positive function. Here W : R → R is a two well potential. Via variational methods, we show that there is layered solution which is heteroclinic in x and periodic in y direction.