Nonlocal eigenvalue problems with indefinite weight (original) (raw)

In the present paper, we consider a class of eigenvalue problems driven by a nonlocal integro-dierential operator \scrL p(x) K with Dirichlet boundary conditions. Under certain assumptions on p and q, we establish that any \lambda > 0 suciently small is an eigenvalue of the nonhomogeneous nonlocal problem (\scrP \lambda). ® §£«ï¤ õâìáï ª« á ᯥªâà «ì¨å § ¤ ç,¯®¢'ï § ¨å ÷ § ¥«®ª «ì¨¬ ÷⥣à®-¤¨ä¥à¥ae÷ «ì¨¬ ®¯¥à â®à®¬ \scrL p(x) K ÷ § ªà ©®¢®î 㬮¢®î ¨à¨å«¥. ¯¥¢¨å ਯãé¥ì 鮤® p ÷ q ¤®¢¥¤¥®, é® ª®¦¥ ¤®áâ ì® ¬ «¥ \lambda > 0 õ ¢« ᨬ § ç¥ï¬ ¥®¤®à÷¤®ù ¥«®ª «ì®ù § ¤ ç÷ (\scrP \lambda).