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- W2884172134 abstract "This study concerns the existence of positive solution for the system [ begin{cases} -Delta u=lambda a(x)f(v),,,,,, xinOmega, -Delta v=lambda b(x)g(u),,,,,, xinOmega, u=v=0,,,,,, xin partial Omega. end{cases} ] where (lambda>0) is a parameter, (Omega) is a bounded domain in (R^N(N > 1)) with smooth boundary (partialOmega) and (Delta) is the Laplacian operator. Here (a(x)) and (b(x)) are (C^1) sign-changing functions that maybe negative near the boundary and (f, g) are (C^1) nondecresing functions such that (f; g : [0;infty) rightarrow [0;infty) ; f(s), g(s) > 0 ; s > 0) and [lim_{xrightarrowinfty}frac{f(Mg(x))}{x}=0] ; for every (M > 0): We discuss the existence of positive solution when (f, g, a(x)) and (b(x)) satisfy certain additional conditions. We use the method of sub-super solutions to establish our results." @default.
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- W2884172134 date "2011-10-21" @default.
- W2884172134 modified "2023-10-14" @default.
- W2884172134 title "A Note On The Existence Of Positive Solution For A Class Of Laplacian Nonlinear System With Sign-changing Weight" @default.
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- W2884172134 doi "https://doi.org/10.22436/jmcs.03.03.07" @default.
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