where urce" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305601&_mathId=si2.gif&_user=111111111&_pii=S0022247X16305601&_rdoc=1&_issn=0022247X&md5=fba70658e884612d99e39c156d66d18a">urce" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16305601-si2.gif">, ulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305601&_mathId=si3.gif&_user=111111111&_pii=S0022247X16305601&_rdoc=1&_issn=0022247X&md5=6e62ae28db1af7f4484190039cb74745" title="Click to view the MathML source">h(x) is a given function and ulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305601&_mathId=si389.gif&_user=111111111&_pii=S0022247X16305601&_rdoc=1&_issn=0022247X&md5=b99b25d843eb6680df846bba38f4d4f5" title="Click to view the MathML source">V(x) has prescribed finitely many singular points. Our goal in this paper is to establish some existence and multiplicity results for above problem when ulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305601&_mathId=si5.gif&_user=111111111&_pii=S0022247X16305601&_rdoc=1&_issn=0022247X&md5=7f67c2b4751677eebb928cb0dc7278a2" title="Click to view the MathML source">μ∈(0,μup>⁎up>) for some ulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305601&_mathId=si6.gif&_user=111111111&_pii=S0022247X16305601&_rdoc=1&_issn=0022247X&md5=e4bde463563ec471611eef99d9371c15" title="Click to view the MathML source">μup>⁎up>>0 and obtain exact estimate for extremal value ulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305601&_mathId=si7.gif&_user=111111111&_pii=S0022247X16305601&_rdoc=1&_issn=0022247X&md5=98029ce6b8ccaa907a2929dcd6d28d0c" title="Click to view the MathML source">μup>⁎up>=μup>⁎up>(Ω,γ,2up>⁎up>,h(x))>0 for above problem.