We consider the following ( p , q )-Laplacian Kirchhoff type problem-( a + b â R 3 | â u | p d x ) "p u-( c + d â R 3 | â u | q d x ) "q u + V ( x ) ( | u | p-2 u + | u | q-2 u ) = K ( x ) f ( u ) in R 3 , where a , b , c , d > 0 are constants, 3 2 < p < q < 3, V : R 3 → R and K : R 3 → R are positive continuous functions allowed for vanishing behavior at infinity, and f is a continuous function with quasicritical growth. Using a minimization argument and a quantitative deformation lemma we establish the existence of nodal solutions.
Nodal solutions for double phase Kirchhoff problems with vanishing potentials
Isernia T.;
2021-01-01
Abstract
We consider the following ( p , q )-Laplacian Kirchhoff type problem-( a + b â R 3 | â u | p d x ) "p u-( c + d â R 3 | â u | q d x ) "q u + V ( x ) ( | u | p-2 u + | u | q-2 u ) = K ( x ) f ( u ) in R 3 , where a , b , c , d > 0 are constants, 3 2 < p < q < 3, V : R 3 → R and K : R 3 → R are positive continuous functions allowed for vanishing behavior at infinity, and f is a continuous function with quasicritical growth. Using a minimization argument and a quantitative deformation lemma we establish the existence of nodal solutions.File in questo prodotto:
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