?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Facta.bibl.u-szeged.hu%2F75804%2F&rft.title=Existence+and+multiplicity+of+nontrivial+solutions+to+the+modified+Kirchhoff+equation+without+the+growth+and+Ambrosetti-Rabinowitz+conditions&rft.creator=+Wang+Zhongxiang&rft.creator=+Jia+Gao&rft.subject=01.+Term%C3%A9szettudom%C3%A1nyok&rft.subject=01.01.+Matematika&rft.description=The+paper+focuses+on+the+modified+Kirchhoff+equation+a+%2B+b+Z+RN+%7C%E2%88%87u%7C+2+dx%EF%BF%BD+%E2%88%86u+%E2%88%92+u%E2%88%86(u+2+)+%2B+V(x)u+%3D+%CE%BB+f(u)%2C+x+%E2%88%88+R+N%2C+where+a%2C+b+%3E+0%2C+V(x)+%E2%88%88+C(RN%2C+R)+and+%CE%BB+%3C+1+is+a+positive+parameter.+We+just+assume+that+the+nonlinearity+f(t)+is+continuous+and+superlinear+in+a+neighborhood+of+t+%3D+0+and+at+infinity.+By+applying+the+perturbation+method+and+using+the+cutoff+function%2C+we+get+existence+and+multiplicity+of+nontrivial+solutions+to+the+revised+equation.+Then+we+use+the+Moser+iteration+to+obtain+existence+and+multiplicity+of+nontrivial+solutions+to+the+above+original+Kirchhoff+equation.+Moreover%2C+the+nonlinearity+f(t)+may+be+supercritical.&rft.date=2021&rft.type=Foly%C3%B3irat&rft.type=NonPeerReviewed&rft.format=full&rft.language=hu&rft.identifier=http%3A%2F%2Facta.bibl.u-szeged.hu%2F75804%2F1%2Fejqtde_2021_083.pdf&rft.identifier=+++Wang+Zhongxiang%3B++Jia+Gao%3A+++Existence+and+multiplicity+of+nontrivial+solutions+to+the+modified+Kirchhoff+equation+without+the+growth+and+Ambrosetti-Rabinowitz+conditions.++(2021)+++&rft.language=eng