Positive Solutions Of Some Semilinear Problems With Sign-changing Weight

This paper studies the existence of positive solutions for some semilinear problem with sign-changing weight.The main results are described as follows:1.We consider the existence of positive solutions of second order elliptic problem on RN where N≥3,λ>0 is a parameter,a:RN→R is sign-changing,f:[0,∞)→R is a continuous function with f(0)>0.Compared with the problem of a bounded domain by D.D.Hai in[J.Math.Anal.Appl.1998],this section extends the problem to the RN.We obtain the existence of positive solutions and the bifurcation behavior of positive solution sets for this problem.2.We consider the existence of positive solutions of boundary value problem for second order difference equation on nonnegative integer set where λ>0 is a parameter,p:[0,∞)z→(0,∞)is a function,b:[0,∞)z→R may change sign,f:[0,∞)→R is continuous with f(0)>0.The main results are the discretization of the results of D.Rajendran and J.Tyagi in[Electron.J.Differ.Equ.2010].3.We consider the existence of positive solutions of boundary value problem for second order difference equation where T>2 is an integer,k>0 is a constant,λ>0 is a parameter,c:[0,T+1]z→R may change sign,f:[0,T+1]z×[0,∞)→[0,∞)is continuous,f(i,0)=0 with the sub-linear growth condition at ∞.We generalize the corresponding results of R.Ma and H.Ma in[J.Difference Equ.Appl.2011].