A Fold Bifurcation Theorem of Degenerate Solutions in a Perturbed Nonlinear Equation

<table>Bifurcation diagram of the equation <svg height="16.637501" id="M122" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 99.625 16.637501" width="99.625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.6375)">
<g transform="translate(72,-58.69)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜆</tspan>
<tspan style="font-size: 12.50px; " x="9.5397892" y="0">−</tspan>
<tspan style="font-size: 12.50px; " x="20.880011" y="0">𝑥</tspan>
</text>
<text transform="matrix(1,0,0,-1,-44.19,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
<text transform="matrix(1,0,0,-1,-36.54,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">−</tspan>
<tspan style="font-size: 12.50px; " x="11.340221" y="0">𝑦</tspan>
</text>
<text transform="matrix(1,0,0,-1,-18.99,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
<text transform="matrix(1,0,0,-1,-10.64,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">0</tspan>
</text>
</g>
</g>
</svg> in Example <a href="https://static.hindawi.com/articles/aaa/volume-2011/302942/figures/#ex2.6">2.6</a>.</table>

Abstract and Applied Analysis

fig1

Figure 1

Figure 1: A Fold Bifurcation Theorem of Degenerate Solutions in a Perturbed Nonlinear Equation 