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Abstract. We develop a generalized quasilinearization method for a forced Duffing equation with three-point nonlinear boundary conditions and obtain two monotone sequences of approximate solutions converging quadratically to the unique solution of the problem.Mathematics subject classification (2000): 34A37, 34B15.

BackgroundAmyotrophic Lateral Sclerosis (ALS) is a rare progressive and chronic motor neuron degenerative disease for which at present no cure is available. In recent years, multiple genes encode kinases and other causative agents for ALS have been identified. Kinases are enzymes that show pleiotropic nature and regulate different signal transduction processes and pathways. The dysregulation of kinase activity results in dramatic changes in processes and causes many other human diseases including cancers.MethodsIn this study, we have adopted a network-based system biology approach to investigate the kinase-based molecular interplay between ALS and other human disorders. A list of 62 ALS-associated-kinases was first identified and then we identified the disease associated with them by scanning multiple disease-gene interaction databases to understand the link between the ALS-associated kinases and other disorders.ResultsAn interaction network with 36 kinases and 381 different disorders associated with them was prepared, which represents the complexity and the comorbidity associated with the kinases. Further, we have identified 5 miRNAs targeting the majority of the kinases in the disease-causing network. The gene ontology and pathways enrichment analysis of those miRNAs were performed to understand their biological and molecular functions along with to identify the important pathways. We also identified 3 drug molecules that can perturb the disease-causing network by drug repurposing.ConclusionThis network-based study presented hereby contributes to a better knowledge of the molecular underpinning of comorbidities associated with the kinases associated with the ALS disease and provides the potential therapeutic targets to disrupt the highly complex disease-causing network.