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Note 6 - Stockholders' Equity (Details Textual) - USD ($)			1 Months Ended	12 Months Ended
	Feb. 20, 2019	Aug. 09, 2017	Mar. 31, 2019	Dec. 31, 2019	Dec. 31, 2018	Sep. 13, 2018	Jun. 30, 2017
Proceeds from Issuance of Common Stock, Net Issuance Costs				$ 2,103,788
Preferred Stock, Par or Stated Value Per Share				$ 0.001	$ 0.001
Adjustments to Additional Paid in Capital, Preferred Stock Beneficial Conversion Feature at Issuance				$ 12,692,308
Adjustments to Additional Paid in Capital, Preferred Stock Beneficial Conversion Feature, Deemed Dividend				(12,692,308)
Temporary Equity, Par Value				13,661,578
Dividends, Common Stock, Total				$ 0
Class of Warrant or Right, Number of Securities Called by Warrants or Rights							2,646,091
Class of Warrant or Right, Exercise Price of Warrants or Rights							$ 7.50
Warrants and Rights Outstanding, Term							10 years
Share-based Compensation Arrangement by Share-based Payment Award, Options, Grants in Period, Gross				714,350	85,000
Share-based Payment Arrangement, Nonvested Award, Option, Cost Not yet Recognized, Amount				$ 2,200,000
Share-based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition				2 years 36 days
Share-based Payment Arrangement, Expense				$ 875,851	$ 841,421
General and Administrative Expense [Member]
Share-based Payment Arrangement, Expense				872,244	827,466
Research and Development Expense [Member]
Share-based Payment Arrangement, Expense				$ 3,607	$ 13,955
The 2018 Incentive Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award, Number of Shares Authorized						1,250,000
Share-based Compensation Arrangement by Share-based Payment Award, Number of Shares Available for Grant				598,650
Share-based Compensation Arrangement by Share-based Payment Award, Options, Grants in Period, Gross				714,350
Share-based Compensation Arrangement by Share-based Payment Award, Options, Granted in Period, Fair Value				$ 2,900,000
The 2018 Incentive Plan [Member] \| Employees [Member] \| Share-based Payment Arrangement, Option [Member]
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Expected Term				6 years
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Expected Volatility Rate				82.00%
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Expected Dividend Rate				0.00%
The 2018 Incentive Plan [Member] \| Employees [Member] \| Share-based Payment Arrangement, Option [Member] \| Minimum [Member]
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Discount Rate				1.90%
The 2018 Incentive Plan [Member] \| Employees [Member] \| Share-based Payment Arrangement, Option [Member] \| Maximum [Member]
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Discount Rate				2.50%
Old PLx Omnibus Stock Option Plan and Dipexium 2013 Equity Incentive Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award, Options, Grants in Period, Gross					85,000
Share-based Compensation Arrangement by Share-based Payment Award, Options, Granted in Period, Fair Value					$ 207,537
Old PLx Omnibus Stock Option Plan and Dipexium 2013 Equity Incentive Plan [Member] \| Employees [Member] \| Share-based Payment Arrangement, Option [Member]
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Expected Term					6 years
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Expected Dividend Rate					0.00%
Old PLx Omnibus Stock Option Plan and Dipexium 2013 Equity Incentive Plan [Member] \| Employees [Member] \| Share-based Payment Arrangement, Option [Member] \| Minimum [Member]
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Discount Rate					2.60%
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Expected Volatility Rate					76.00%
Old PLx Omnibus Stock Option Plan and Dipexium 2013 Equity Incentive Plan [Member] \| Employees [Member] \| Share-based Payment Arrangement, Option [Member] \| Maximum [Member]
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Discount Rate					2.80%
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Expected Volatility Rate					82.00%
Warrants Issued in Connection with Term Loan Facility [Member]
Class of Warrant or Right, Number of Securities Called by Warrants or Rights		58,502
Class of Warrant or Right, Exercise Price of Warrants or Rights		$ 6.41
Class of Warrant or Right, Term		10 years
Series A Preferred Stock [Member]
Stock Issued During Period, Shares, New Issues	15,000
Proceeds from Issuance of Private Placement	$ 15,000,000
Preferred Stock, Par or Stated Value Per Share	$ 0.001
Shares Issued, Price Per Share	1,000
Preferred Stock, Convertible, Conversion Price	$ 2.60
Preferred Stock, Dividend Rate, Percentage	8.00%
Preferred Stock, Liquidation Preference, Value	$ 1,000
Adjustments to Additional Paid in Capital, Preferred Stock Beneficial Conversion Feature at Issuance				$ 12,700,000
Adjustments to Additional Paid in Capital, Preferred Stock Beneficial Conversion Feature, Deemed Dividend				12,700,000
Temporary Equity, Par Value				13,700,000
Payments of Stock Issuance Costs				1,300,000
Dividends, Preferred Stock, Total				$ 1,100,000
Preferred Stock, Dividends Per Share, Declared				$ 70.57
JMP Securities, Inc [Member]
Distribution Agreement, Aggregate Sales Price			$ 12,500,000
Public Offering Price Allowed under Shelf Registration, Total			$ 75,000,000
Stock Issued During Period, Shares, New Issues				398,709
Proceeds from Issuance of Common Stock				$ 2,300,000
Proceeds from Issuance of Common Stock, Net Issuance Costs				2,100,000
Distribution Agreement, Amount Available for Sale				$ 10,200,000