In this paper, we consider the existence of positive solutions of second-order periodic boundary value problem where 0 〈 ε 〈 1/2, g ： [0, 2π] →R is continuous, f ： [0, ∞） →R is continuous and λ 〉 0 is a pa...In this paper, we consider the existence of positive solutions of second-order periodic boundary value problem where 0 〈 ε 〈 1/2, g ： [0, 2π] →R is continuous, f ： [0, ∞） →R is continuous and λ 〉 0 is a parameter.展开更多
The existence, multiplicity and uniqueness of positive solutions of a third order two point boundary value problem are discussed with the help of two fixed point theorems in cones, respectively.
In this paper, we establish two existence theorems of twin positive solutions for a class of nonlinear second-order three-point boundary value problems, and concentrate on the case when nonlinear term does not satisfy...In this paper, we establish two existence theorems of twin positive solutions for a class of nonlinear second-order three-point boundary value problems, and concentrate on the case when nonlinear term does not satisfy usual conditions.展开更多
In this paper, we investigate the existence of positive solutions for the singular fourth-order differential system <em>u</em><sup>(4)</sup> = <em><span style="white-space:nowrap;...In this paper, we investigate the existence of positive solutions for the singular fourth-order differential system <em>u</em><sup>(4)</sup> = <em><span style="white-space:nowrap;">φ</span>u</em> + <em>f </em>(<em>t</em>, <em>u</em>, <em>u</em>”, <em><span style="white-space:nowrap;">φ</span></em>), 0 < <em>t</em> < 1, -<em><span style="white-space:nowrap;">φ</span></em>” = <em>μg</em> (<em>t</em>, <em>u</em>, <em>u</em>”), 0 < <em>t</em> < 1, <em>u</em> (0) = <em>u</em> (1) = <em>u</em>”(0) = <em>u</em>”(1) = 0, <em><span style="white-space:nowrap;">φ</span> </em>(0) = <em><span style="white-space:nowrap;">φ</span> </em>(1) = 0;where <em>μ</em> > 0 is a constant, and the nonlinear terms<em> f</em>, <em>g</em> may be singular with respect to both the time and space variables. The results obtained herein generalize and improve some known results including singular and non-singular cases.展开更多
A class of nonlinear neutral equations with positive and negative coefficients is considered. Seveal conditions for existence of eventually positive solutions are obtained,and they extend and improve some of the crite...A class of nonlinear neutral equations with positive and negative coefficients is considered. Seveal conditions for existence of eventually positive solutions are obtained,and they extend and improve some of the criteria existing in literature. Our conditions are necessary and suffcient when all the coeffcients of the equations are constants.展开更多
By using fixed point index theory, we consider the existence of positive solutions for singular nonlinear Neumann boundary value problems. Our main results extend and improve many known results even for non-singular c...By using fixed point index theory, we consider the existence of positive solutions for singular nonlinear Neumann boundary value problems. Our main results extend and improve many known results even for non-singular cases.展开更多
In this paper, we prove the existence of at least one positive solution pairto the following semilinear elliptic systemby using a linking theorem, where K（x）is a positive function in L^s（R^N） for some s 〉 1and th...In this paper, we prove the existence of at least one positive solution pairto the following semilinear elliptic systemby using a linking theorem, where K（x）is a positive function in L^s（R^N） for some s 〉 1and the nonnegative functions f, g ∈ C（R, R） are of quasicritical growth, superlinear atinfinity. We do not assume that f or g satisfies the Ambrosetti-Rabinowitz condition as usual. Our main result can be viewed as a partial extension of a recent result of Alves, Souto and Montenegro in [1] concerning the existence of a positive solution to the following semilinear elliptic problemand a recent result of Li and Wang in [22] concerning the existence of nontrivial solutions to a semilinear elliptic system of Hamiltonian type in R^N.展开更多
In this paper, a fixed-point theorem has been used to investigate the existence of countable positive solutions of n-point boundary value problem. As an application, we also give an example to demonstrate our results.
In this paper, we study a semilinear elliptic equation defined on a bounded smooth domain. This type of problem arises from the study of spatial ecology model, and the growth function in the equation has a strong Alle...In this paper, we study a semilinear elliptic equation defined on a bounded smooth domain. This type of problem arises from the study of spatial ecology model, and the growth function in the equation has a strong Allee effect and is inhomogeneous. We use variational methods to prove that the equation has at least two positive solutions for a large parameter if it satisfies some appropriate conditions. We also prove some nonexistence results.展开更多
基金Supported by the National Natural Science Foundation of China(No.11321627,11401479,71561024,11561063)China Postdoctoral Science Foundation(2014M562472)+1 种基金Postdoctoral Science Foundation of Gansu Provincethe Science Research Project for Colleges and Universities of Gansu Province(2016A-003)
文摘In this paper, we consider the existence of positive solutions of second-order periodic boundary value problem where 0 〈 ε 〈 1/2, g ： [0, 2π] →R is continuous, f ： [0, ∞） →R is continuous and λ 〉 0 is a parameter.
文摘The existence, multiplicity and uniqueness of positive solutions of a third order two point boundary value problem are discussed with the help of two fixed point theorems in cones, respectively.
文摘In this paper, we establish two existence theorems of twin positive solutions for a class of nonlinear second-order three-point boundary value problems, and concentrate on the case when nonlinear term does not satisfy usual conditions.
文摘In this paper, we investigate the existence of positive solutions for the singular fourth-order differential system <em>u</em><sup>(4)</sup> = <em><span style="white-space:nowrap;">φ</span>u</em> + <em>f </em>(<em>t</em>, <em>u</em>, <em>u</em>”, <em><span style="white-space:nowrap;">φ</span></em>), 0 < <em>t</em> < 1, -<em><span style="white-space:nowrap;">φ</span></em>” = <em>μg</em> (<em>t</em>, <em>u</em>, <em>u</em>”), 0 < <em>t</em> < 1, <em>u</em> (0) = <em>u</em> (1) = <em>u</em>”(0) = <em>u</em>”(1) = 0, <em><span style="white-space:nowrap;">φ</span> </em>(0) = <em><span style="white-space:nowrap;">φ</span> </em>(1) = 0;where <em>μ</em> > 0 is a constant, and the nonlinear terms<em> f</em>, <em>g</em> may be singular with respect to both the time and space variables. The results obtained herein generalize and improve some known results including singular and non-singular cases.
文摘A class of nonlinear neutral equations with positive and negative coefficients is considered. Seveal conditions for existence of eventually positive solutions are obtained,and they extend and improve some of the criteria existing in literature. Our conditions are necessary and suffcient when all the coeffcients of the equations are constants.
基金Project supported by NSFC(10471075) NSFSP(Y2003A01, J02P01, XJ03001).
文摘By using fixed point index theory, we consider the existence of positive solutions for singular nonlinear Neumann boundary value problems. Our main results extend and improve many known results even for non-singular cases.
基金supported by NSFC(11071095)Hubei Key Laboratory of Mathematical Sciences
文摘In this paper, we prove the existence of at least one positive solution pairto the following semilinear elliptic systemby using a linking theorem, where K（x）is a positive function in L^s（R^N） for some s 〉 1and the nonnegative functions f, g ∈ C（R, R） are of quasicritical growth, superlinear atinfinity. We do not assume that f or g satisfies the Ambrosetti-Rabinowitz condition as usual. Our main result can be viewed as a partial extension of a recent result of Alves, Souto and Montenegro in [1] concerning the existence of a positive solution to the following semilinear elliptic problemand a recent result of Li and Wang in [22] concerning the existence of nontrivial solutions to a semilinear elliptic system of Hamiltonian type in R^N.
文摘In this paper, a fixed-point theorem has been used to investigate the existence of countable positive solutions of n-point boundary value problem. As an application, we also give an example to demonstrate our results.
基金supported by the National Natural Science Foundation of China (No.10671049)the US-NSF grants (No.DMS-0314736)
文摘In this paper, we study a semilinear elliptic equation defined on a bounded smooth domain. This type of problem arises from the study of spatial ecology model, and the growth function in the equation has a strong Allee effect and is inhomogeneous. We use variational methods to prove that the equation has at least two positive solutions for a large parameter if it satisfies some appropriate conditions. We also prove some nonexistence results.
