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Nonlinear periodic problems superlinear at $+\infty$ and sublinear at $-\infty$
Abstract
We consider a nonlinear periodic problem driven by a nonlinear, nonhomogeneous
differential operator with a reaction which exhibits an asymmetric growth at
$+\infty$ and at $-\infty$. It is $\left( p-1\right) -$superlinear near
$+\infty$ and $\left( p-1\right) -$ sublinear near $-\infty$. A particular
case of our problem is that of periodic equations with the scalar $p-$
Laplacian and an asymmetric nonlinearity. Using variational methods and Morse
theory, we prove the existence of at least three nontrivial solutions.
differential operator with a reaction which exhibits an asymmetric growth at
$+\infty$ and at $-\infty$. It is $\left( p-1\right) -$superlinear near
$+\infty$ and $\left( p-1\right) -$ sublinear near $-\infty$. A particular
case of our problem is that of periodic equations with the scalar $p-$
Laplacian and an asymmetric nonlinearity. Using variational methods and Morse
theory, we prove the existence of at least three nontrivial solutions.
Keywords
Asymmetric reaction, nonhomogeneous differential opertator, C-condition, critical groups, homotopy equivalent, mountain pass theorem.
DOI: http://dx.doi.org/10.14510%2Flm-ns.v33i1.48