English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

<p>The  two-point boundary value problem for second-order differential inclusions of  the form <mml:math alttext="$(D/dt)dot{m}(t)in F(t,m(t),dot{m}(t))$">  <mml:mrow>  <mml:mrow><mml:mo>(</mml:mo>  <mml:mrow>  <mml:mrow><mml:mi>D</mml:mi><mml:mo>/</mml:mo><mml:mrow>  <mml:mi>d</mml:mi><mml:mi>t</mml:mi>  </mml:mrow></mml:mrow>  </mml:mrow>  <mml:mo>)</mml:mo></mml:mrow><mml:mover accent='true'>  <mml:mi>m</mml:mi>  <mml:mo>&#x02D9;</mml:mo>  </mml:mover>  <mml:mrow><mml:mo>(</mml:mo>  <mml:mi>t</mml:mi>  <mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2208;</mml:mo><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo>  <mml:mrow>  <mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mrow><mml:mo>(</mml:mo>  <mml:mi>t</mml:mi>  <mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mover accent='true'>  <mml:mi>m</mml:mi>  <mml:mo>&#x02D9;</mml:mo>  </mml:mover>  <mml:mrow><mml:mo>(</mml:mo>  <mml:mi>t</mml:mi>  <mml:mo>)</mml:mo></mml:mrow>  </mml:mrow>  <mml:mo>)</mml:mo></mml:mrow>  </mml:mrow> </mml:math> on complete Riemannian manifolds is investigated for a couple of points, nonconjugate along at least one geodesic of  Levi-Civitá connection, where <mml:math alttext="$D/dt$">  <mml:mrow><mml:mi>D</mml:mi><mml:mo>/</mml:mo><mml:mrow>  <mml:mi>d</mml:mi><mml:mi>t</mml:mi>  </mml:mrow></mml:mrow> </mml:math> is the covariant derivative of Levi-Civitá connection and <mml:math alttext="$F(t,m,X)$">  <mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo>  <mml:mrow>  <mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>X</mml:mi>  </mml:mrow>  <mml:mo>)</mml:mo></mml:mrow> </mml:math> is a set-valued vector with quadratic or less than quadratic growth in the third argument. Some interrelations between certain geometric characteristics, the distance between points, and the norm of right-hand side are found that guarantee solvability of the above problem for <mml:math alttext="$F$">  <mml:mi>F</mml:mi> </mml:math> with quadratic growth in <mml:math alttext="$X$">  <mml:mi>X</mml:mi> </mml:math>. It is shown that this interrelation holds for all inclusions with <mml:math alttext="$F$">  <mml:mi>F</mml:mi> </mml:math> having less than quadratic growth in <mml:math alttext="$X$">  <mml:mi>X</mml:mi> </mml:math>, and so for them the problem is solvable.</p

On the two-point boundary value problem for quadratic second-order differential equations and inclusions on manifolds