{'fraction_non_alphanumeric': 0.017857142857142856, 'fraction_numerical': 0.001984126984126984, 'mean_word_length': 4.9411764705882355, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
The Bifurcation and Decay of Solutions for Asymptotically Linear Elliptic Systems with Parameter

This paper deals with an elliptic system of the form  where N≥3, λ is a parameter, and  is a weighted function. We employ the Rabinowitz’s global bifurcation theory and the Dancer’s unilateral global bifurcation theory to determine the existence of positive solution and negative solution on the interval of  with respect to λ. Furthermore, we also provide the decay of the positive and negative solutions.