Does anyone have idea of application support models frameworks and best practice? Are there any books on this

Second for COBIT5 and ITIL V3. ITIL would not specifically include 'application support' in its terminology but rather consider application delivery within the framework of service delivery. Common sense has to be applied in the application of ITIL.

How you approach this might depend on your goals. Are you transitioning an application? Do you have issues with availability? Are you implementing a new application? Do you wish to improve the level of support on one of your current applications? Is there an SLA in place? Do you have a service catalogue? 

The answers to those questions will determine how you should apply ITIL in your case.

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COBIT 5 provides a comprehensive framework for IT governance. ITIL V3 provides a comprehensive framework for IT service management.  CMMi provides a comprehensive framework for software development process.