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We refer to $f(x)$ as {\\it weight} and to $F(u)$ as {\\it nonlinearity}. The remarkable fact is that if the weight function is bounded from below by a strict positive constant that is $0<C\\le f$ then it does not have much impact on the stable solutions, however, a nonnegative weight that is $0\\le f$ will push certain critical dimensions. 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We refer to $f(x)$ as {\\it weight} and to $F(u)$ as {\\it nonlinearity}. The remarkable fact is that if the weight function is bounded from below by a strict positive constant that is $0<C\\le f$ then it does not have much impact on the stable solutions, however, a nonnegative weight that is $0\\le f$ will push certain critical dimensions. 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