Journal ArticleDOI
On a singular nonlinear semilinear elliptic problem
Junping Shi,Miaoxin Yao +1 more
TLDR
In this article, the singular boundary value problem is considered and the existence, uniqueness, regularity and the dependency on parameters of the positive solutions under various assumptions are investigated under the same assumptions.Abstract:
We consider the singular boundary value problemWe study the existence, uniqueness, regularity and the dependency on parameters of the positive solutions under various assumptions.read more
Citations
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Journal ArticleDOI
Exact Multiplicity of Positive Solutions for a Class of Semilinear Problem, II
Tiancheng Ouyang,Junping Shi +1 more
TL;DR: In this paper, the exact shape of the global bifurcation diagram is rigorously proved for a wide class of nonlinear functions ǫ(u)/ǫ.
Journal ArticleDOI
Combined Effects of Singular and Superlinear Nonlinearities in Some Singular Boundary Value Problems
TL;DR: In this article, a class of singular semilinear elliptic Dirichlet boundary value problems where the combined effects of a superlinear and a singular term allow us to establish some existence and multiplicity results is studied.
Journal ArticleDOI
Multiplicity and asymptotic behavior of positive solutions for a singular semilinear elliptic problem
TL;DR: In this paper, the singular elliptic boundary value problem is studied and the existence, multiplicity and asymptotic behavior of solutions of this problem are discussed by combining variational and sub-supersolution methods.
Journal ArticleDOI
Persistence in reaction diffusion models with weak allee effect
TL;DR: In this paper, the positive steady state distributions and dynamical behavior of reaction-diffusion equation with weak Allee effect type growth were studied, in which the growth rate per capita is not monotonic as in logistic type, and the habitat is assumed to be a heterogeneous bounded region.
Journal ArticleDOI
Diffusive logistic equation with constant yield harvesting, I: Steady states
TL;DR: In this paper, the authors consider a reaction-diffusion equation which models the constant yield harvesting to a spatially heterogeneous population which satisfies a logistic growth and prove the existence, uniqueness and stability of the maximal steady state solutions under certain conditions.
References
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Book
Elliptic Partial Differential Equations of Second Order
David Gilbarg,Neil S. Trudinger +1 more
TL;DR: In this article, Leray-Schauder and Harnack this article considered the Dirichlet Problem for Poisson's Equation and showed that it is a special case of Divergence Form Operators.
Journal ArticleDOI
Combined Effects of Concave and Convex Nonlinearities in Some Elliptic Problems
TL;DR: In this article, a class of semilinear elliptic Dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results is considered.
Journal ArticleDOI
On a dirichlet problem with a singular nonlinearity
TL;DR: In this article, a dirichlet problem with singular nonlinearity is considered, and the authors present a communication in Partial Differential Equations (PDE) approach to solve it.
Journal ArticleDOI
On a singular nonlinear elliptic boundary-value problem
Alan C. Lazer,P. J. McKenna +1 more
TL;DR: In this paper, the authors considered the singular boundary value problem with the assumption that p(x) > 0 and certain smoothness assumptions, and showed that there exists a solution which is smooth on Q2 and continuous on Q.
Journal ArticleDOI
A Nonlinear Singular Boundary Value Problem in the Theory of Pseudoplastic Fluids
A. Nachman,A. Callegari +1 more
TL;DR: In this article, boundary layer equations for the class of non-Newtonian fluids termed pseudoplastic are examined under the classical conditions of uniform flow past a semi-infinite flat plate.