Solutions to General Quasilinear Elliptic Second Order Problems (original) (raw)

Existence of solutions for some degenerate quasilinear elliptic equations

Le Matematiche, 2009

In this paper we are interested in the existence of solutions for Dirichlet problem associated to the degenerate quasilinear elliptic equations − n ∑ j=1 D j [ω(x)A j (x, u, ∇u)] + ω(x)g(x, u(x), ∇u(x)) = f 0 − n ∑ j=1 D j f j , on Ω, in the setting of the weighted Sobolev spaces W 1,p 0 (Ω, ω).

Existence of solution for a generalized quasilinear elliptic problem

Journal of Mathematical Physics, 2017

It establishes existence and multiplicity of solutions to the elliptic quasilinear Schrödinger equation −div(g2(u)∇u)+g(u)g′(u)|∇u|2+V(x)u=h(x,u),x∈ℝN,where g, h, V are suitable smooth functions. The function g is asymptotically linear at infinity and, for each fixed x∈ℝN, the function h(x, s) behaves like s at the origin and s3 at infinity. In the proofs, we apply variational methods.

The Existence of Multiple Solutions to Quasilinear Elliptic Equations

Bulletin of the London Mathematical Society, 2005

Using Morse theory and the truncation technique, a proof is given of the existence of at least three nontrivial solutions for a class of p-Laplacian equations. When p = 2, the existence of four nontrivial solutions is also considered.

Dirichlet problem for quasi-linear elliptic equations

2000

We study the Dirichlet Problem associated to the quasilinear elliptic problem n X i=1 @ @xi A i(x;u(x);ru(x)) +B(x;u(x);ru(x)) = 0: Then we dene a potential theory related to this problem and we show that the sheaf of continuous solutions satises the Bauer axiomatic theory.

Some Qualitative Properties of Solutions of Quasilinear Elliptic Equations and Applications

Journal of Differential Equations, 2001

We study quasilinear elliptic equations of Leray Lions type in W 1, p (0), maximum principles, nonexistence and existence of solutions, the control of lower (upper) bound for essential supremum (essential infimum) of solutions, sign-changing solutions, local and global oscillation of solutions, geometry of domain, generating singularities of solutions, and lower bounds on constants appearing in Schauder, Agmon, Douglis, and Nirenberg estimates.