Periodicity, Stability, and Boundedness of Solutions to Certain Second Order Delay Differential Equations

<div>Function <svg height="12.7178pt" id="M425" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 20.4818 12.7178" width="20.4818pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,8.352,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,12.85,0)"><path d="M170 255C170 288 146 313 114 313S58 288 58 255C58 221 82 198 114 198S170 221 170 255Z" id="g113-46"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="228" vert-adv-y="228"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,15.814,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g></svg>.</div>

International Journal of Differential Equations

fig4

Figure 4

Figure 4: Periodicity, Stability, and Boundedness of Solutions to Certain Second Order Delay Differential Equations 