In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive superlinear integro-differential equations on the half line by means of the fixed poi...In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive superlinear integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.展开更多
It is to establish existence of a weak solution for quasilinear elliptic problems assuming that the nonlinear term is critical.The potential V is bounded from below and above by positive constants.Because we are consi...It is to establish existence of a weak solution for quasilinear elliptic problems assuming that the nonlinear term is critical.The potential V is bounded from below and above by positive constants.Because we are considering a critical term which interacts with higher eigenvalues for the linear problem,we need to apply a linking theorem.Notice that the lack of compactness,which comes from critical problems and the fact that we are working in the whole space,are some obstacles for us to ensure existence of solutions for quasilinear elliptic problems.The main feature in this article is to restore some compact results which are essential in variational methods.Recall that compactness conditions such as the Palais-Smale condition for the associated energy functional is not available in our setting.This difficulty is overcame by taking into account some fine estimates on the critical level for an auxiliary energy functional.展开更多
Using Riccati transformation techniques,some oscillation criteria for the forced second-order superlinear difference equations are established.These criteria are dis- crete analogues of the criteria for differential e...Using Riccati transformation techniques,some oscillation criteria for the forced second-order superlinear difference equations are established.These criteria are dis- crete analogues of the criteria for differential equations proposed by Yan.展开更多
In this paper, we use cone theory and topological degree theory to study superlinear systemof integral equations, and obtain existence theorems for non-trivial solutions; moreover, we applythe results to two-point bo...In this paper, we use cone theory and topological degree theory to study superlinear systemof integral equations, and obtain existence theorems for non-trivial solutions; moreover, we applythe results to two-point boundary problems of ordinary differential system of equations.展开更多
In this paper, first a priori bounds for positive solutions of superlinear system of elliptic boundary value problem is estimated, then the fixed point index theory is used to investigate the existence of solutions.
文摘In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive superlinear integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.
基金partially supported by CNPq with(429955/2018-9)partially suported by CNPq(309026/2020-2)FAPDF with(16809.78.45403.25042017)。
文摘It is to establish existence of a weak solution for quasilinear elliptic problems assuming that the nonlinear term is critical.The potential V is bounded from below and above by positive constants.Because we are considering a critical term which interacts with higher eigenvalues for the linear problem,we need to apply a linking theorem.Notice that the lack of compactness,which comes from critical problems and the fact that we are working in the whole space,are some obstacles for us to ensure existence of solutions for quasilinear elliptic problems.The main feature in this article is to restore some compact results which are essential in variational methods.Recall that compactness conditions such as the Palais-Smale condition for the associated energy functional is not available in our setting.This difficulty is overcame by taking into account some fine estimates on the critical level for an auxiliary energy functional.
基金This research was partially supported by the NNSF of China (Grant 10626032,10771118)NSF of Shandong (Grant Y2005A06).
文摘Using Riccati transformation techniques,some oscillation criteria for the forced second-order superlinear difference equations are established.These criteria are dis- crete analogues of the criteria for differential equations proposed by Yan.
文摘In this paper, we use cone theory and topological degree theory to study superlinear systemof integral equations, and obtain existence theorems for non-trivial solutions; moreover, we applythe results to two-point boundary problems of ordinary differential system of equations.
文摘In this paper, first a priori bounds for positive solutions of superlinear system of elliptic boundary value problem is estimated, then the fixed point index theory is used to investigate the existence of solutions.
