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We consider the existence of positive solutions of the singular nonlinear semipositone problem of the form $\{\begin{matrix} - {div (| x |}^{- α p} {| \nabla u |}^{p - 2} {\nabla u) = | x |}^{- (α + 1) p + β} (a u^{p - 1} - f (u) - \frac{c}{u^{γ}}), x \in Ω, \\ u = 0, x \in \partial Ω, \end{matrix}$ where $Ω$ is a bounded smooth domain of $ℝ^{N}$ with $0 \in Ω$ , $1 < p < N$ , $0 \leq α < (N - p) / p$ , $γ \in (0, 1)$ , and $a$ , $β$ , $c$ and $λ$ are positive parameters. Here $f : [0, \infty) \to ℝ$ is a continuous function. This model arises in the studies of population biology of one species with $u$ representing the concentration of the species. We discuss the existence of a positive solution when $f$ satisfies certain additional conditions. We use the method of sub-supersolutions...

A posteriori error estimate of approximate solutions to a mildly nonlinear elliptic boundary value problem

Juraj Weisz (1990)

Commentationes Mathematicae Universitatis Carolinae

A posteriori error estimates for nonlinear problems. $L^{r}$ -estimates for finite element discretizations of elliptic equations

R. Verfürth (1998)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

A Primal Hybrid Finite Element Method for Quasilinear Second Order Elliptic Problems.

Fabio A. Milner (1985)

Numerische Mathematik

A priori Bounds and necessary conditions for solvability of prescribed curvature equations.

Neil S. Trudinger (1990)

Manuscripta mathematica

A priori bounds for solutions of parabolic problems and applications

Pavol Quittner (2002)

Mathematica Bohemica

We review some recent results concerning a priori bounds for solutions of superlinear parabolic problems and their applications.

In this survey we consider superlinear parabolic problems which possess both blowing-up and global solutions and we study a priori estimates of global solutions.

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A note on the solvability of nonlinear elliptic problems with jumping nonlinearities

A numerically based investigation on the symmetry breaking and asymptotic behavior of the ground states to the $p$ -Hénon equation.

A parallel splitting-up method for partial differential equations and its applications to Navier-Stokes equations

A perspective on the contributions of Alan C. Lazer to critical point theory.

A population biological model with a singular nonlinearity

A posteriori error estimate of approximate solutions to a mildly nonlinear elliptic boundary value problem

A posteriori error estimates for nonlinear problems. $L^{r}$ -estimates for finite element discretizations of elliptic equations

A Primal Hybrid Finite Element Method for Quasilinear Second Order Elliptic Problems.

A priori Bounds and necessary conditions for solvability of prescribed curvature equations.

A priori bounds for solutions of parabolic problems and applications

A priori bounds for solutions of parabolic problems and applications

A priori estimates for global solutions and multiple equilibria of a superlinear parabolic problem involving measures.

A Priori estimates for minimal surfaces with free boundary, which are not minima of the area.

A priori estimates of solutions of superlinear problems

A priori-Schranken für diskrete Lösungen monotoner Operatorgleichungen und Anwendungen.

A remark on Fefferman's equation in non-smooth domains.

A remark on some nonlinear elliptic problems.

A remark on the solvability of the Dirichlet problem in Sobolev spaces with power-type weights

A remark on uniqueness for quasilinear elliptic equations

A saddle point theorem for non-smooth functionals and problems at resonance.

Currently displaying 41 – 60 of 851