EXISTENCE OF SOLUTIONS FOR ASYMPTOTICALLY ‘LINEAR’ -LAPLACIAN EQUATIONS

SHIBO LIU; SHUJIE LI

doi:10.1112/S0024609303002546

Abstract

Under very general conditions, a proof is given, via Morse theory, of the existence of solutions for asymptotically ‘linear’ $p$-Laplacian equations, where the asymptotic limit may be greater than the second eigenvalue. The existence of nonzero solutions is also considered.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Cossio, Jorge and Herrón, Sigifredo 2008. Existence of radial solutions for an asymptotically linear p-Laplacian problem. Journal of Mathematical Analysis and Applications, Vol. 345, Issue. 1, p. 583.

Duc, Duong Minh Loc, Nguyen Hoang and Phi, Le Long 2008. Nonlinear versions of Stampacchia and Lax–Milgram theorems and applications to -Laplace equations. Nonlinear Analysis: Theory, Methods & Applications, Vol. 68, Issue. 4, p. 925.

Fang, Fei and Liu, Shibo 2009. Nontrivial solutions of superlinear p-Laplacian equations. Journal of Mathematical Analysis and Applications, Vol. 351, Issue. 1, p. 138.

Tanaka, Mieko 2009. Existence of a non-trivial solution for the -Laplacian equation with Fučík type resonance at infinity. II. Nonlinear Analysis: Theory, Methods & Applications, Vol. 71, Issue. 7-8, p. 3018.

Tanaka, Mieko 2010. Existence of a non-trivial solution for the -Laplacian equation with Fučík-type resonance at infinity, III. Nonlinear Analysis: Theory, Methods & Applications, Vol. 72, Issue. 1, p. 507.

Motreanu, Dumitru Motreanu, Viorica V. and Papageorgiou, Nikolaos S. 2010. Existence and multiplicity of solutions for asymptotically linear, noncoercive elliptic equations. Monatshefte für Mathematik, Vol. 159, Issue. 1-2, p. 59.

Gasiński, Leszek and Papageorgiou, Nikolaos S. 2012. Multiple solutions for asymptotically (p−1)-homogeneous p-Laplacian equations. Journal of Functional Analysis, Vol. 262, Issue. 5, p. 2403.

Sun, Juan and Liu, Shibo 2012. Nontrivial solutions of Kirchhoff type problems. Applied Mathematics Letters, Vol. 25, Issue. 3, p. 500.

Bartolo, Rossella Candela, Anna Maria and Salvatore, Addolorata 2013. p-Laplacian problems with nonlinearities interacting with the spectrum. Nonlinear Differential Equations and Applications NoDEA, Vol. 20, Issue. 5, p. 1701.

TAN, ZHONG and FANG, FEI 2013. NONTRIVIAL SOLUTIONS FOR N-LAPLACIAN EQUATIONS WITH SUB-EXPONENTIAL GROWTH. Analysis and Applications, Vol. 11, Issue. 03, p. 1350005.

Bartolo, R. 2014. Multiplicity Results for a Class of Quasilinear Elliptic Problems. Mediterranean Journal of Mathematics, Vol. 11, Issue. 4, p. 1099.

Candela, Anna Maria and Palmieri, Giuliana 2014. Analysis and Topology in Nonlinear Differential Equations. Vol. 85, Issue. , p. 175.

Gasiński, Leszek and Papageorgiou, Nikolaos S. 2015. Resonant equations with the Neumann p-Laplacian plus an indefinite potential. Journal of Mathematical Analysis and Applications, Vol. 422, Issue. 2, p. 1146.

Candela, A.M. Palmieri, G. and Perera, K. 2015. Multiple solutions for p-Laplacian type problems with asymptotically p-linear terms via a cohomological index theory. Journal of Differential Equations, Vol. 259, Issue. 1, p. 235.

Ait-Mahiout, K. Djebali, S. and Moussaoui, T. 2016. Multiple solutions for a BVP on $${(0,+\infty)}$$ ( 0 , + ∞ ) via Morse theory and $${H^1_{0,p}(\mathbb{R}^+)}$$ H 0 , p 1 ( R + ) versus $${C^1_{p}(\mathbb{R}^+)}$$ C p 1 ( R + ) local minimizers. Arabian Journal of Mathematics, Vol. 5, Issue. 1, p. 9.

Candela, A. M. and Palmieri, G. 2017. Multiplicity results for some nonlinear elliptic problems with asymptotically $${{\varvec{p}}}$$ p -linear terms. Calculus of Variations and Partial Differential Equations, Vol. 56, Issue. 3,

Liu, Guanggang Li, Yong and Yang, Xue 2018. Rotating periodic solutions for super-linear second order Hamiltonian systems. Applied Mathematics Letters, Vol. 79, Issue. , p. 73.

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EXISTENCE OF SOLUTIONS FOR ASYMPTOTICALLY ‘LINEAR’ ${p}$-LAPLACIAN EQUATIONS

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EXISTENCE OF SOLUTIONS FOR ASYMPTOTICALLY ‘LINEAR’ ${p}$-LAPLACIAN EQUATIONS

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