文摘
We consider a semilinear Robin problem driven by the Laplacian plus an indefinite potential and with a Carathéodory reaction class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302464&_mathId=si1.gif&_user=111111111&_pii=S0893965916302464&_rdoc=1&_issn=08939659&md5=88eb064d9c63bf29ff08a2889e4e382d" title="Click to view the MathML source">f(z,x)class="mathContainer hidden">class="mathCode"> with no growth restriction on the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302464&_mathId=si2.gif&_user=111111111&_pii=S0893965916302464&_rdoc=1&_issn=08939659&md5=026159a68209c0610870ee6ecdbd9e93" title="Click to view the MathML source">xclass="mathContainer hidden">class="mathCode">-variable. We only assume that class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302464&_mathId=si3.gif&_user=111111111&_pii=S0893965916302464&_rdoc=1&_issn=08939659&md5=471db93d58795b27573cbb5ef4798218" title="Click to view the MathML source">f(z,⋅)class="mathContainer hidden">class="mathCode"> is odd and superlinear near zero. Using a variant of the symmetric mountain pass theorem, we show that the problem has a whole sequence of distinct smooth nodal solutions converging to the trivial one.