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Existence of Positive Stationary Solutions and Threshold Results for a Reaction–Diffusion System☆
The systemu1t−Δu1=u1u2−bu1,u2t−Δu2=au1inΩ×(0, T), whereΩ⊂Rnis a smooth bounded domain, with homogeneous Dirichlet boundary conditionsu1=u2=0 on ∂Ω×(0, T) and initial conditionsu1(x, 0),u2(x, 0), isExpand
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A Short Note on Quenching Phenomena for Semilinear Parabolic Equations
Abstract In this paper, we investigate initial–boundary value problems for semilinear parabolic differential equations with singular term. A criterion for the appearance of quencing phenomena ofExpand
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Positive solutions for non-homogeneous semilinear elliptic equations with data that changes sign
Let Ω ⊂ R N be a bounded domain. We consider the nonlinear problem and prove that the existence of positive solutions of the above nonlinear problem is closely related to the existence ofExpand
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A priori estimates, existence and non-existence of positive solutions of generalized mean curvature
Abstract This paper concerns a priori estimates and existence of solutions of generalized mean curvature equations with Dirichlet boundary value conditions in smooth domains. Using the blow-up methodExpand
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Uniqueness and stability of positive steady state solutions for a ratio-dependent predator–prey system with a crowding term in the prey equation
Abstract This paper deals with a ratio-dependent predator–prey system with a crowding term in the prey equation, where it is assumed that the coefficient of the functional response is less than theExpand
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Global existence and decay estimates for solutions of degenerate parabolic equations
AbstractIn this paper, we will show the existence and certain decay estimate of the global solutions for the initial-boundary value problem $$\left\{ {\begin{array}{*{20}c} {u_t - \frac{d}{{dx_iExpand
Existence and the dynamical behaviors of the positive solutions for a ratio-dependent predator–prey system with the crowing term and the weak growth
Abstract This paper deals with a ratio-dependent predator–prey system with the crowing term and the weak growth in the prey equation. Under the condition that the coefficient λ is less than aExpand
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