One Dimensional $p$-Laplacian with a Concentrated Nonlinear Source
نویسندگان
چکیده
منابع مشابه
Positive solutions for one-dimensional p-Laplacian boundary value problems with nonlinear parameter
In this paper, we establish existence of positive solutions of the nonlinear problems of one dimensional p-Laplacian with nonlinear parameter φp(u ′(t))′ + a(t)f(λ, u) = 0, t ∈ (0, 1), u(0) = u(1) = 0. where a : Ω→ R is continuous and may change sign, λ > 0 is a parameter, f(λ, 0) > 0 for all λ > 0. By applying Leray-Schauder fixed point theorem we obtain the existence of positive solutions.
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We study a nonlinear ordinary second order vector equation of pLaplacian type under nonlinear boundary conditions. Applying Leray-Schauder arguments we obtain solutions under appropriate conditions. Moreover, for the scalar case we prove the existence of at least one periodic solution of the problem applying the method of upper and lower solutions. INTRODUCTION We consider a nonlinear one-dimen...
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We also prove that the lower bound is sharp. Eigenvalue problems for quasilinear operators of p-Laplace type like (1.1) have received considerable attention in the last years (see, e.g., [1, 2, 3, 5, 8, 13]). The asymptotic behavior of eigenvalues was obtained in [6, 7]. Lyapunov inequalities have proved to be useful tools in the study of qualitative nature of solutions of ordinary linear diffe...
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We study the existence of the weak solution of the nonlinear boundary-value problem −(|u′|p−2u′)′ = λ|u|p−2u+ g(u)− h(x) in (0, π), u(0) = u(π) = 0 , where p and λ are real numbers, p > 1, h ∈ Lp (0, π) (p′ = p p−1 ) and the nonlinearity g : R → R is a continuous function of the Landesman-Lazer type. Our sufficiency conditions generalize the results published previously about the solvability of...
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ژورنال
عنوان ژورنال: Bulletin of the Belgian Mathematical Society - Simon Stevin
سال: 2012
ISSN: 1370-1444
DOI: 10.36045/bbms/1337864271