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.; Repovs, D. D.. - In: ASYMPTOTIC ANALYSIS. - ISSN 0921-7134. - 124:3-4(2021), pp. 371-396. [10.3233/ASY-201648]

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.
2021
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/294874
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