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Via critical point theory we establish the existence and regularity of solutions for the quasilinear elliptic problem ⎧ $d i v (x, \nabla u) + {a (x) | u |}^{p - 2} u = {g (x) | u |}^{p - 2} u + h (x) {| u |}^{s - 1} u$ in $ℝ^{N}$ ⎨ ⎩ u > 0, $l i m_{| x | \to \infty} u (x) = 0$ , where 1 < p < N; a(x) is assumed to satisfy a coercivity condition; h(x) and g(x) are not necessarily bounded but satisfy some integrability restrictions.

p-harmonic equation and quasiregular mappings

B. Bojarski, T. Iwaniec (1987)

Banach Center Publications

Phenomena of compensation and estimates for partial differential equations.

Hélein, Frédéric (1998)

Documenta Mathematica

Phragmén-Lindelöf and nonexistence theorems for nonlinear elliptic equations.

Patricio Aviles (1983)

Manuscripta mathematica

Picone's identity and the moving plane procedure.

Allegretto, Walter, Siegel, David (1995)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Picone’s identity for a Finsler $p$ -Laplacian and comparison of nonlinear elliptic equations

Jaroslav Jaroš (2014)

Mathematica Bohemica

In the paper we present an identity of the Picone type for a class of nonlinear differential operators of the second order involving an arbitrary norm $H$ in $ℝ^{n}$ which is continuously differentiable for $x \neq 0$ and such that $H^{p}$ is strictly convex for some $p > 1$ . Two important special cases are the $p$ -Laplacian and the so-called pseudo $p$ -Laplacian. The identity is then used to establish a variety of comparison results concerning nonlinear degenerate elliptic equations which involve such operators. We also get criteria...

Picone-type inequalities for nonlinear elliptic equations and their applications.

Jaroš, Jaroslav, Takaŝi, Kusano, Yoshida, Norio (2001)

Journal of Inequalities and Applications [electronic only]

Picone-type inequalities for nonlinear elliptic equations with first-order terms and their applications.

Jaroš, Jaroslav, Takaŝi, Kusano, Yoshida, Norio (2006)

Journal of Inequalities and Applications [electronic only]

Piecewise bilinear preconditioning of high-order finite element method.

Kim, Sang Dong (2007)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Piecewise linear wavelet collocation, approximation of the boundary manifold, and quadrature.

Ehrich, S., Rathsfeld, A. (2001)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Plane wave discontinuous Galerkin methods: Analysis of the h-version

Claude J. Gittelson, Ralf Hiptmair, Ilaria Perugia (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

We are concerned with a finite element approximation for time-harmonic wave propagation governed by the Helmholtz equation. The usually oscillatory behavior of solutions, along with numerical dispersion, render standard finite element methods grossly inefficient already in medium-frequency regimes. As an alternative, methods that incorporate information about the solution in the form of plane waves have been proposed. We focus on a class of Trefftz-type discontinuous Galerkin methods that ...

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Perturbations near resonance for the $p$ -Laplacian in $ℝ^{N}$ .

Perturbations singulières coercives : réduction à des perturbations régulières et applications

Perturbations singulières et noyaux de Poisson

Perturbations singulières et noyaux de Poisson pour les opérateurs frontières homogènes

Perturbations singulières relatives au problème de Dirichlet dans un demi-espace

Perturbatively unstable eigenvalues of a periodic Schrödinger operator.

Perturbed nonlinear degenerate problems in $ℝ^{N}$