Making Aliyah to Israel while leaving one’s parents in the Diaspora:
If one desires to permanently move to Eretz Yisrael, and his parents do not want him to do so, then some Poskim rule that he is not required to listen to his parents and may go ahead and move to Israel. Certainly, one may move to Israel if his parents do not voice any protest. Other Poskim, however, rule to the contrary that one may not leave his parents alone in the Diaspora even for the sake of moving to Israel, and even if they do not protest his move. Practically, if one’s parents need the son to stay with them in order to care for them, then he should not move.
 Pesakim Teshuvos 240:46
 Maharam Merothenberg 28; 79; Mabit 1:139, brought in Shiyurei Kneses Hagedola 240:28; Peas HaShulchan 2:21; Mel Tzedaka 26; See Rashi end of Parshas Noach regarding Avraham; Maharsha Kesubos 111a; Mishpitei Aretz 11:5 leaves this matter in question
 Beis Shlomo Y.D. 2:94 based on Rishonim who rule that the Mitzvah to live in Israel is not an obligation; Panim Yafos Bereishis 12; Binas Adam on Mishpitei Aretz 11:3; See Pischeiy Teshuvah E.H. 75:6; Sefer Hamakneh Kiddushin 31b; Vayoel Moshe Mamar Yishuv Eretz Yisrael 81
 Pesakim Teshuvos ibid; See Sefer Nishmas Kol Chaiy 1:48; Maaseh Avraham Y.D. 43