TY - JOUR
T1 - On p(x)-Laplacian equations in RN with nonlinearity sublinear at zero
AU - Liu, Shibo
AU - Zhao, Chunshan
N1 - Publisher Copyright:
© Orthogonal Publisher and Springer Nature Switzerland AG 2025.
PY - 2025/6/2
Y1 - 2025/6/2
N2 - Let p, q be functions on RN satisfying 1≪q≪p≪N, we consider p(x)-Laplacian problems of the form (Formula presented.) To apply variational methods, we introduce a subspace X of W1,p(x)(RN) as our working space. Compact embedding from X into Lq(x)(RN) is established, this enable us to get nontrivial solution of the problem; and two sequences of solutions going to ∞ and 0 respectively, when g(x,·) is odd.
AB - Let p, q be functions on RN satisfying 1≪q≪p≪N, we consider p(x)-Laplacian problems of the form (Formula presented.) To apply variational methods, we introduce a subspace X of W1,p(x)(RN) as our working space. Compact embedding from X into Lq(x)(RN) is established, this enable us to get nontrivial solution of the problem; and two sequences of solutions going to ∞ and 0 respectively, when g(x,·) is odd.
KW - Mountain pass theorem
KW - Palais-smale condition
KW - p(x)-Laplacian
KW - p(x)-Sublinear
UR - http://www.scopus.com/inward/record.url?scp=105007084480&partnerID=8YFLogxK
U2 - 10.1007/s41808-025-00346-3
DO - 10.1007/s41808-025-00346-3
M3 - Article
AN - SCOPUS:105007084480
SN - 2296-9020
JO - Journal of Elliptic and Parabolic Equations
JF - Journal of Elliptic and Parabolic Equations
ER -