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On the principal eigenvalue of some nonlocal diffusion problems
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
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Boundary blow-up solutions to elliptic systems of competitive type
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 boundaryExpand
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Maximum and Comparison Principles for Operators Involving thep-Laplacian
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. SomeExpand
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Boundary behavior for large solutions to elliptic equations with singular weights
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 growthExpand
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Uniqueness and asymptotic behaviour for solutions of semilinear problems with boundary blow-up
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. MoreExpand
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Fujita exponents for evolution problems with nonlocal diffusion
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 \inExpand
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Uniqueness and boundary behavior of large solutions to elliptic problems with singular weights
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
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Large solutions for an elliptic system of quasilinear equations
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-LaplacianExpand
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A Local Bifurcation Theorem for Degenerate Elliptic Equations With Radial Symmetry
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} beingExpand
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Pointwise Growth and Uniqueness of Positive Solutions for a Class of Sublinear Elliptic Problems where Bifurcation from Infinity Occurs
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 functionExpand
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