Nodal solutions for double phase Kirchhoff problems with vanishing potentials

Abstract

We consider the following ( p , q )-Laplacian Kirchhoff type problem − ( a + b ∫ R 3 | ∇ u | p d x ) Δ p u − ( c + d ∫ R 3 | ∇ u | q d x ) Δ 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.

Existence of constant sign and nodal solutions for a class of (p,q)-Laplacian-Kirchhoff problems

“…Inspired by the facts above and [23,24], we here demonstrate the existence of three solutions to problem (1.1) by applying the Nehari manifold along with truncation and comparison techniques, and critical point theory, which presents the novelty of the research on problem (1.1). As far as we know, there are few results on the (p, q)-Laplacian Kirchhoff type equations [23,25], but there are no results on multiple solutions to problem (1.1). So this work may be the first result in this direction.…”

Existence of solution to singular Schrödinger systems involving the fractional p‐Laplacian with Trudinger–Moser nonlinearity in ℝN

“…Do et al 13 studied the nonautonomous fractional Hamiltonian system with critical exponential growth in R via Linking Theorem and Galerkin approximation procedure. For more results on (p, q)-fractional Laplace system, (p, q)-fractional Laplace equation, we recommend the readers to previous works [14][15][16][17][18][19][20][21][22] for details information. I thank the reviewers for recommending that references.…”

Multiplicity and concentration of solutions to fractional anisotropic Schrödinger equations with exponential growth

“…where ε > 0 is a parameter, s ∈ (0, 1), 1 < p < q < N s and f has the subcritical growth and satisfies some suitable conditions. For more results on fractional ( p, q)-Laplace or ( p, q)-Laplace, we refer the readers to [9][10][11]. When s → 1 −1 , the Eq.…”