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On the principal eigenvalue of some nonlocal diffusion problems

- J. García-Melián, J. Rossi
- Mathematics
- 2009

Abstract In this paper we analyze some properties of the principal eigenvalue λ 1 ( Ω ) of the nonlocal Dirichlet problem ( J ∗ u ) ( x ) − u ( x ) = − λ u ( x ) in Ω with u ( x ) = 0 in R N ∖ Ω .… Expand

77 6- PDF

Boundary blow-up solutions to elliptic systems of competitive type

- J. García-Melián, J. Rossi
- Mathematics
- 1 November 2004

Abstract We consider the elliptic system Δ u = u p v q , Δ v = u r v s in Ω , where p , s > 1 , q , r > 0 , and Ω ⊂ R N is a smooth bounded domain, subject to different types of Dirichlet boundary… Expand

60 6

Maximum and Comparison Principles for Operators Involving thep-Laplacian

- J. García-Melián, J. S. D. Lis
- Mathematics
- 1 February 1998

Abstract In this paper some characterizations for the validity of both maximum and weak comparison principles for the operator L pu = −Δpu + a(x)|u|p − 2u, under Dirichlet conditions, are given. Some… Expand

84 6

Boundary behavior for large solutions to elliptic equations with singular weights

- J. García-Melián
- Mathematics
- 1 August 2007

Abstract In this paper we analyze the boundary behavior of large positive solutions to some semilinear elliptic equations which include a singular weight. The most important point is that the growth… Expand

49 5

Uniqueness and asymptotic behaviour for solutions of semilinear problems with boundary blow-up

- J. García-Melián, R. Letelier-Albornoz, J. S. D. Lis
- Mathematics
- 6 June 2001

In this paper we prove uniqueness of positive solutions to logistic singular problems −∆u = λ(x)u − a(x)up, u|∂Ω = +∞, p > 1, a > 0 in Ω, where the main feature is the fact that a|∂Ω = 0. More… Expand

135 3- PDF

Fujita exponents for evolution problems with nonlocal diffusion

- J. García-Melián, F. Quirós
- Mathematics
- 1 March 2010

AbstractWe prove the existence of a critical exponent of Fujita type for the nonlocal diffusion problem
$$\left\{\begin{array}{l@{\quad}l}u_t(x, t) = J*u(x, t)-u(x, t) + u^p(x, t), & \qquad x \in… Expand

26 3

Uniqueness and boundary behavior of large solutions to elliptic problems with singular weights

- M. Chuaqui, C. Cortázar, M. Elgueta, J. García-Melián
- Mathematics
- 1 September 2004

We consider the elliptic problems $\Delta u=a(x)u^m$, $m>1$, and
$\Delta u=a(x)e^u$ in a smooth bounded domain $\Omega$, with the
boundary condition $u=+\infty$ on $\partial\Omega$. The weight … Expand

65 2- PDF

Large solutions for an elliptic system of quasilinear equations

- J. García-Melián
- Mathematics
- 15 December 2008

In this paper we consider the quasilinear elliptic system Δpu=uavb, Δpv=ucve in a smooth bounded domain Ω⊂RN, with the boundary conditions u=v=+∞ on ∂Ω. The operator Δp stands for the p-Laplacian… Expand

21 2- PDF

A Local Bifurcation Theorem for Degenerate Elliptic Equations With Radial Symmetry

- J. García-Melián, J. S. D. Lis
- Mathematics
- 10 February 2002

Abstract In this work we provide local bifurcation results for equations involving the p-Laplacian in balls. We analyze the continua C n of radial solutions emanating from (λn, p, 0), {λn, p} being… Expand

23 2

Pointwise Growth and Uniqueness of Positive Solutions for a Class of Sublinear Elliptic Problems where Bifurcation from Infinity Occurs

- J. García-Melián, R. Gómez-Reñasco, J. López-Gómez, J. C. Sabina de Lis
- Mathematics
- 1 December 1998

Abstract.In this paper we analyze the uniqueness and the pointwise growth of the positive solutions of a nonlinear elliptic boundary‐value problem of general sublinear type with a weight function… Expand

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