Exact Asymptotic Expansion of Singular Solutions for the (<svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.738pt;width:45.212502px;" id="M1" height="15.6125" version="1.1" viewBox="0 0 45.212502 15.6125" width="45.212502">
	
		
			<g transform="matrix(.022,-0,0,-.022,.062,15.487)"><path id="x1D7D0" d="M453 211h25l-46 -211h-415v23q97 102 151 166q42 49 81 110q51 78 51 148q0 56 -31.5 91.5t-87.5 35.5q-77 0 -122 -90h-28q67 204 223 204q82 0 132 -49.5t50 -133.5q0 -110 -114 -218l-162 -154h140q82 0 107 13q27 13 46 65z"></path></g><g transform="matrix(.022,-0,0,-.022,16.247,15.487)"><path id="x2B" d="M535 230h-212v-233h-58v233h-213v50h213v210h58v-210h212v-50z"></path></g><g transform="matrix(.022,-0,0,-.022,34.382,15.487)"><path id="x31" d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z"></path></g>

		
	
</svg>)-D Protter Problem

<table>All orthogonality conditions fulfilled for <svg height="13.125" id="M354" style="vertical-align:-1.95624pt" version="1.1" viewbox="0 0 58.325001 13.125" width="58.325001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.125)">
<g transform="translate(72,-61.5)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑘</tspan>
<tspan style="font-size: 12.50px; " x="10.239957" y="0">≤</tspan>
<tspan style="font-size: 12.50px; " x="22.280346" y="0">[</tspan>
<tspan style="font-size: 12.50px; " x="26.443846" y="0">𝑛</tspan>
<tspan style="font-size: 12.50px; " x="32.657837" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="36.133671" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="42.38517" y="0">]</tspan>
</text>
</g>
</g>
</svg>.</table>

Abstract and Applied Analysis

fig5

Figure 5

Figure 5: Exact Asymptotic Expansion of Singular Solutions for the (<svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.738pt;width:45.212502px;" id="M1" height="15.6125" version="1.1" viewBox="0 0 45.212502 15.6125" width="45.212502">
	
		
			<g transform="matrix(.022,-0,0,-.022,.062,15.487)"><path id="x1D7D0" d="M453 211h25l-46 -211h-415v23q97 102 151 166q42 49 81 110q51 78 51 148q0 56 -31.5 91.5t-87.5 35.5q-77 0 -122 -90h-28q67 204 223 204q82 0 132 -49.5t50 -133.5q0 -110 -114 -218l-162 -154h140q82 0 107 13q27 13 46 65z"></path></g><g transform="matrix(.022,-0,0,-.022,16.247,15.487)"><path id="x2B" d="M535 230h-212v-233h-58v233h-213v50h213v210h58v-210h212v-50z"></path></g><g transform="matrix(.022,-0,0,-.022,34.382,15.487)"><path id="x31" d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z"></path></g>

		
	
</svg>)-D Protter Problem 

Abstract and Applied Analysis

Exact Asymptotic Expansion of Singular Solutions for the ( )-D Protter Problem

Figure 5

Exact Asymptotic Expansion of Singular Solutions for the ()-D Protter Problem