We derive a priori bounds for positive supersolutions of $-\Delta_p u = \rho(x) f(u)$, where p >1 and $\Delta_p$ is the p-Laplace operator, in a smooth bounded domain of $\mathbb{R}^N$ with zero Dirichlet boundary conditions. We apply our results to the nonlinear elliptic eigenvalue problem $-\Delta_p u = \lambda f(u)$, with Dirichlet boundary condition, where $f$ is a nondecreasing continuous differentiable function on such that f(0)>0, $f(t) ^{1/(p-1)}$ is superlinear at infinity, and give sharp upper and lower bounds for the extremal parameter $\lambda_p^* $. In particular, we consider the nonlinearities $f(u) = e^u $ and $f(u)=(1+u) ^m$ ($ m > p-1$) and give explicit estimates on $\lambda_p^*$. As a by-product of our resu...
We prove the existence of positive classical solutions for the p-Laplacian problem $$\displaylines...
We investigate the asymptotic behaviour as p→∞ of sequences of solutions of the equation View the M...
Abstract. This study concerns the existence and stability properties of positive weak solutions to c...
We consider the Dirichlet problem for positive solutions of the equation $-Delta_p (u) = f(u)$ in a...
We study the existence of positive solutions for perturbations of the classical eigenvalue problem ...
Using a combination of several methods, such as variational methods. the sub and supersolutions meth...
Abstract. In this paper, we study a class of boundary value prob-lem involving the p-Laplacian oprat...
We study one-dimensional p-Laplacian problems and answer the unsolved problem. Our method is to stud...
This paper gives a survey over the existence of uniform L∞ a priori bounds for positive solutions of...
AbstractUsing a combination of several methods, such as variational methods, the sub and supersoluti...
The aim of this paper is investigating the existence and the multiplicity of solutions of a quasilin...
The goal of this paper is to study the multiplicity of positive solutions of a class of quasilinear ...
In this dissertation, we study the existence and nonexistence of positive solutions to some classes ...
We consider the quasilinear degenerate elliptic equation lambda u - Delta(p)u + H(x, Du) = 0 in Omeg...
We prove the existence of positive solutions for the p-Laplacian problem [formula] where [formula] c...
We prove the existence of positive classical solutions for the p-Laplacian problem $$\displaylines...
We investigate the asymptotic behaviour as p→∞ of sequences of solutions of the equation View the M...
Abstract. This study concerns the existence and stability properties of positive weak solutions to c...
We consider the Dirichlet problem for positive solutions of the equation $-Delta_p (u) = f(u)$ in a...
We study the existence of positive solutions for perturbations of the classical eigenvalue problem ...
Using a combination of several methods, such as variational methods. the sub and supersolutions meth...
Abstract. In this paper, we study a class of boundary value prob-lem involving the p-Laplacian oprat...
We study one-dimensional p-Laplacian problems and answer the unsolved problem. Our method is to stud...
This paper gives a survey over the existence of uniform L∞ a priori bounds for positive solutions of...
AbstractUsing a combination of several methods, such as variational methods, the sub and supersoluti...
The aim of this paper is investigating the existence and the multiplicity of solutions of a quasilin...
The goal of this paper is to study the multiplicity of positive solutions of a class of quasilinear ...
In this dissertation, we study the existence and nonexistence of positive solutions to some classes ...
We consider the quasilinear degenerate elliptic equation lambda u - Delta(p)u + H(x, Du) = 0 in Omeg...
We prove the existence of positive solutions for the p-Laplacian problem [formula] where [formula] c...
We prove the existence of positive classical solutions for the p-Laplacian problem $$\displaylines...
We investigate the asymptotic behaviour as p→∞ of sequences of solutions of the equation View the M...
Abstract. This study concerns the existence and stability properties of positive weak solutions to c...