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We investigate the following quasilinear and singular problem, $t o 2.7 c m \{\begin{matrix} - Δ_{p} u = \frac{λ}{u^{δ}} + u^{q} & in Ω; \\ {u |}_{\partial Ω} = 0, u > 0 & in Ω, \end{matrix} t o 2.7 c m (P)$ where $Ω$ is an open bounded domain with smooth boundary, $1 < p < \infty$ , $p - 1 < q \leq p^{*} - 1$ , $λ > 0$ , and $0 < δ < 1$ . As usual, $p^{*} = \frac{N p}{N - p}$ if $1 < p < N$ , $p^{*} \in (p, \infty)$ is arbitrarily large if $p = N$ , and $p^{*} = \infty$ if $p > N$ . We employ variational methods in order to show the existence of at least two distinct (positive) solutions of problem (P) in $W_{0}^{1, p} (Ω)$ . While following an approach due to Ambrosetti-Brezis-Cerami, we need to prove two new results of separate interest: a strong comparison principle and a regularity result for solutions...

Solutions positives d'équations elliptiques non linéaires avec exposant de Sobolev critique et conjecture de Rellich pour les surfaces à courbure moyenne prescrite

H. Brezis (1982/1983)

Séminaire Équations aux dérivées partielles (Polytechnique)

Solutions to $H$ -systems by topological and iterative methods.

Amster, P., Mariani, M. C. (2003)

Abstract and Applied Analysis

Solutions to nonlinear elliptic equations with a nonlocal boundary condition.

Wang, Yuandi (2002)

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

Solutions with prescribed periods on the boundary components on non-linear elliptic systems of first order in multiply connected domains in the plane

Wolfgang Tutschke (1983)

Banach Center Publications

Solvability of degenerate elliptic boundary value problems: another approach

Alois Kufner, Salvatore Leonardi (1994)

Mathematica Bohemica

Using a Hardy-type inequality, the authors weaken certain assumptions from the paper [1] and derive existence results for equations with a stronger degeneration.

Solvability of nonlinear problems at resonance

Pavel Drábek (1982)

Commentationes Mathematicae Universitatis Carolinae

Solvability of semilinear equations with strong nonlinearities and applications to elliptic boundary value problems

Petronije S. Milojević (1987)

Commentationes Mathematicae Universitatis Carolinae

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Displaying 21 – 40 of 88

Singular limits for the bi-laplacian operator with exponential nonlinearity in $R^{4}$

Singular sets and number of solutions of nonlinear boundary value problems

Singularity theory and the geometry of a nonlinear elliptic equation

Smoothness of global positive branches of nonlinear elliptic problems over symmetric domains.

Sobolev versus Hölder local minimizers and existence of multiple solutions for a singular quasilinear equation

Solution Brances of a semilinear elliptic problem at corak-2 Bifurcation points.

Solution Manifolds and Submanifolds of Parametrized Equations and Their Discretization Errors.

Solution of subsonic rotational nonviscous flow in three-dimensional axially symmetric channels [Abstract of thesis]

Solutions numériques de problèmes de bifurcation

Solutions of elliptic equations involving critical Sobolev exponents with Neumann boundary conditions.

Solutions of elliptic equations with indefinite nonlinearities via Morse theory and linking

Solutions of the constraint equations in general relativity satisfying "hyperboloidal boundary conditions" [Book]

Solutions positives de l’équation $- Δ u = u^{p} + μ u^{q}$ dans un domaine à trou