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Spreading speed of a food-limited population model with delay
This paper is concerned with the spreading speed of a food-limited population model with delay. First, the existence of the solution of Cauchy...
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Spreading Speed in the Fisher-KPP Equation with Nonlocal Delay
This paper is concerned with the Fisher-KPP equation with diffusion and nonlocal delay. Firstly, we establish the global existence and uniform...
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Approximate Analytical Solution of the Generalized Kolmogorov-Petrovsky-Piskunov Equation with Cubic Nonlinearity
In this paper, the approximate analytical oscillatory solutions to the generalized Kolmogorov-Petrovsky-Piskunov equation (gKPPE for short) are...
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A Comparison Theorem for Nonsmooth Nonlinear Operators
We prove a comparison theorem for super- and sub-solutions with non-vanishing gradients to semilinear PDEs provided a nonlinearity f is L p function...
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A Weak Comparison Principle for Some Quasilinear Elliptic Operators: It Compares Functions Belonging to Different Spaces
We shall prove a weak comparison principle for quasilinear elliptic operators −div( a ( x ,∇ u )) that includes the negative p -Laplace operator, where a : ×...
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The Boundary Harnack Principle for Nonlocal Elliptic Operators in Non-divergence Form
We prove a boundary Harnack inequality for nonlocal elliptic operators L in non-divergence form with bounded measurable coefficients. Namely, our...
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Weakly coupled systems of parabolic Hamilton–Jacobi equations with Caputo time derivative
In this paper we prove existence and uniqueness of bounded viscosity solutions of weakly coupled systems of parabolic Hamilton–Jacobi equations with...
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A Type of Brézis–Oswald Problem to the \({\Phi}\)- Laplacian Operator with Very Singular Term
In this work we consider existence and uniqueness of solutions for a quasilinear elliptic problem, which may be singular at the origin. Furthermore,...
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On a dynamic boundary condition for singular degenerate parabolic equations in a half space
We consider the initial value problem for a fully-nonlinear degenerate parabolic equation with a dynamic boundary condition in a half space. Our...
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Global existence and blow up of solutions for two classes of reaction diffusion systems with two nonlinear source terms in bounded domain
In this paper we deal with the initial boundary value problem for two classes of reaction diffusion systems with two source terms in bounded domain....
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One-dimensional symmetry and Liouville type results for the fourth order Allen-Cahn equation in ℝ N
In this paper, the authors prove an analogue of Gibbons’ conjecture for the extended fourth order Allen-Cahn equation in ℝ N , as well as Liouville...
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Existence and uniqueness for p-Laplace equations involving singular nonlinearities
We consider quasilinear elliptic equations involving the p -Laplacian and singular nonlinearities. We prove comparison principles and we deduce some...
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A Class of Second-Order Linear Elliptic Equations with Drift: Renormalized Solutions, Uniqueness and Homogenization
In this paper a class of N -dimensional second-order linear elliptic equations with a drift is studied. When the drift belongs to L ...
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Viscosity solutions to a parabolic inhomogeneous equation associated with infinity Laplacian
We obtain the existence and uniqueness results of viscosity solutions to the initial and boundary value problem for a nonlinear degenerate and...
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A Liouville comparison principle for sub- and super-solutions of the equation w t −Δ p (w) = |w| q-1 w
We establish a Liouville comparison principle for entire weak sub- and super-solutions of the equation (*) w t −Δ p ( w ) = | w | q -1 w in the half-space
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On well-posedness of the semilinear heat equation on the sphere
We are concerned with existence, uniqueness and nonuniqueness of nonnegative solutions to the semilinear heat equation in open subsets of the n -dimens...
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Stability of a Nonlinear Equation Related to a Spatially-inhomogeneous Branching Process
Consider the nonlinear equation $$\frac{\partial}{\partial...