where 16305601&_mathId=si2.gif&_user=111111111&_pii=S0022247X16305601&_rdoc=1&_issn=0022247X&md5=fba70658e884612d99e39c156d66d18a">16305601-si2.gif">, 16305601&_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 16305601&_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 16305601&_mathId=si5.gif&_user=111111111&_pii=S0022247X16305601&_rdoc=1&_issn=0022247X&md5=7f67c2b4751677eebb928cb0dc7278a2" title="Click to view the MathML source">μ∈(0,μ⁎) for some 16305601&_mathId=si6.gif&_user=111111111&_pii=S0022247X16305601&_rdoc=1&_issn=0022247X&md5=e4bde463563ec471611eef99d9371c15" title="Click to view the MathML source">μ⁎>0 and obtain exact estimate for extremal value 16305601&_mathId=si7.gif&_user=111111111&_pii=S0022247X16305601&_rdoc=1&_issn=0022247X&md5=98029ce6b8ccaa907a2929dcd6d28d0c" title="Click to view the MathML source">μ⁎=μ⁎(Ω,γ,2⁎,h(x))>0 for above problem.