One-dimensional jumping problem involving p-Laplacian
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We get one theorem which shows existence of solutions for one-dimensional jumping problem involving $p$-Laplacian and Dirichlet boundary condition. This theorem is that there exists at least one solution when nonlinearities crossing finite number of eigenvalues, exactly one solutions and no solution depending on the source term. We obtain these results by the eigenvalues and the corresponding normalized eigenfunctions of the $p-$Laplacian eigenvalue problem when $1<p<\infty$, variational reduction method and Leray-Schauder degree theory when $2\le p<\infty$.
Abstract
We get one theorem which shows existence of solutions for one-dimensional jumping problem involving $p$-Laplacian and Dirichlet boundary condition. This theorem is that there exists at least one solution when nonlinearities crossing finite number of eigenvalues, exactly one solutions and no solution depending on the source term. We obtain these results by the eigenvalues and the corresponding normalized eigenfunctions of the $p-$Laplacian eigenvalue problem when $1<p<\infty$, variational reduction method and Leray-Schauder degree theory when $2\le p<\infty$.
참고문헌 (13)
- Q. H. Choi, "A nonlinear suspension bridge equation with noncon-stant load", Nonlinear Analysis TMA, 35, pp.649~668 (1999)
- Q. H. Choi, "An application of a variational reduction method to a nonlinear wave equation", J. Diff. Eq, 117, pp.390~410 (1995)
- Q. H. Choi, "Multiplicity results for the nonlinear suspension bridge equation, Dynamics of Continuous, Discrete and Impulsive Systems Series A", Mathematical Analysis, 9, pp.29~38 (2002)
- Q. H. Choi, "The study of a nonlinear suspen-sion bridge equation by a variational reduction method", Applicable Analysis, 50, pp.73~92 (1993)
- M. Ghergu, "Singular elliptic problems, bifurcation and as-ymptotic analysis, Oxford Lecture Series in Mathematics and Its Applications", Oxford University Press
- Y. -H. Kim, "Global bifurcation for a class of degenerate elliptic equations with variable exponents", J. Math. Anal Appl, 371, pp.624~637 (2010)
- A. Le, "Eigenvalue Problems for the p-Laplacian", Nonlinear Analysis, 64, pp.1057~1099 (2006)
- R. Manasevich, "Periodic solutions for nonlinear systems with p-Laplacian-like operators", J. Differential Equations, 145, pp.367~393 (1998)
- R. Manasevich, "Boundary value problems for nonlinear perturbations of vector p-Laplacian-like operators", J. Korean Math. Society, 37, pp.665~685 (2000)
- P. J. McKenna, "Nonlinear oscillations in a suspension bridge", Arch. Rat. Mech. Anal, 98, pp.167~177 (1987)
- D. O'Regan, "Some general existence principles and results for (Φ(y0))0 =qf(t; y; y0) 0 < t < 1", SIAM J. Math. Anal, 24, pp.648~668 (1993)
- M. del Pino, "homotopic deformation along p of a Leray Schauder degree result and existence for (ju0jp-2u0)0 + f(x; u) = 0, u(0) = u(T) = 0, p > 1", J. Differential Equations, 80, pp.1~13 (1898)
- S. Solimini, "Some remarks on the number of solutions of some nonlinear ellipltic problems", Ann. Inst. Henri Poincare, 2(2), pp.143~156 (1985)