
beharren auf
to insist on
To persist stubbornly and unyieldingly in an opinion, position, or demand.
Er beharrte auf seiner Meinung, obwohl alle anderen anderer Ansicht waren.
He insisted on his opinion, although everyone else had a different view.
to insist
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to insist on
To persist stubbornly and unyieldingly in an opinion, position, or demand.
Er beharrte auf seiner Meinung, obwohl alle anderen anderer Ansicht waren.
He insisted on his opinion, although everyone else had a different view.

to remain
(elevated, rare) To remain in a place or state; not to yield.
Trotz des Sturms beharrte der Leuchtturmwärter auf seinem Posten.
Despite the storm, the lighthouse keeper remained at his post.
'Beharren' (to insist) is an inseparable verb. The prefix 'be-' remains firmly attached to the verb stem 'harren' in all tenses and sentence constructions.
Sie beharrte darauf, die Rechnung sofort zu bezahlen.
She insisted on paying the bill immediately.
In the meaning 'auf etwas bestehen' (to insist on something), 'beharren' (to insist) is almost always used with the preposition 'auf' and the dative. You insist on something.
Der Anwalt beharrte auf dem Recht seines Mandanten.
The lawyer insisted on his client's right.
People typically 'beharren' (insist) on abstract things such as an opinion, a position, a right, a demand, or a principle.
Trotz der Kritik beharrte der Politiker auf seinem Standpunkt.
Despite the criticism, the politician insisted on his position.
The meaning 'an einem Ort verweilen' (to remain in a place) is very rare today and is used almost only in literary or elevated texts. In everyday language, you almost exclusively encounter 'beharren auf' (to insist on).
Der Soldat beharrte auf seinem Wachtposten, bis die Ablösung kam.
The soldier remained at his guard post until the relief arrived.
to pass / consist / exist
Auf etwas bestehen and auf etwas beharren can both express holding firm to a demand. Bestehen auf can assert a claim neutrally but emphatically; beharren auf emphasizes more strongly that someone stubbornly refuses to give in despite resistance.

Trotz aller Gegenvorschläge beharrt der Kunde auf der vereinbarten Lieferung bis Freitag.
Despite all the counterproposals, the customer insists on the agreed-upon delivery by Friday.
Der Kunde besteht auf der vereinbarten Lieferung bis Freitag.
The customer insists on the agreed-upon delivery by Friday.