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Bifurcation and one-sign solutions of the $p$-Laplacian involving a nonlinearity with zeros

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  • In this paper, we use bifurcation method to investigate the existence and multiplicity of one-sign solutions of the $p$-Laplacian involving a linear/superlinear nonlinearity with zeros. To do this, we first establish a bifurcation theorem from infinity for nonlinear operator equation with homogeneous operator. To deal with the superlinear case, we establish several topological results involving superior limit.
    Mathematics Subject Classification: Primary: 47J15, 47J05; Secondary: 35J60, 35B40.


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