Results 41 to 50 of about 94 (85)
Picone-type identity for pseudo p-Laplacian with variable power
Electronic Journal of Differential Equations, 2012 A Picone type identity is established for homogeneous differential operators involving the pseudo p-Laplacian with variable exponent p=p(x). Using this identity, it is shown that the classical Sturmian theory extends to the associated partial ...
Gabriella Bognar, Ondrej Dosly
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$S$-shaped component of nodal solutions for problem involving one-dimension mean curvature operator
, 2023 summary:Let $E=\{u\in C^1[0,1] \colon u(0)=u(1)=0\}$. Let $S_k^\nu $ with $\nu =\{+, -\}$ denote the set of functions $u\in E$ which have exactly $k-1$ interior nodal zeros in (0, 1) and $\nu u$ be positive near $0$.
He, Zhiqian, Ma, Ruyun, Su, Xiaoxiao
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Picone-type inequalities for nonlinear elliptic equations and their applications
Journal of Inequalities and Applications, 2001 Picone-type inequalities are derived for nonlinear elliptic equations, and Sturmian comparison theorems are established as applications. Oscillation theorems for forced super-linear elliptic equations and superlinear-sublinear elliptic equations are ...
Takaŝi Kusano +2 more
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Sturmian theory and disconjugacy of second order systems
, 1984 A generalization of the Sturm Comparison Theorem is given to second order linear systems. In addition, an analogue to Sternberg disconjugacy criterion for nonselfadjoint second order linear systems is given.
Fozi M. Dannan
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The Picone identity for a class of partial differential equations [PDF]
, 2001 summary:The Picone-type identity for the half-linear second order partial differential equation \[ \sum _{i=1}^n\frac{\partial }{\partial x_i} \Phi \bigg (\frac{\partial u}{\partial x_i}\bigg )+c(x)\Phi (u)=0,\quad \Phi (u):=|u|^{p-2}u,\ p>1, \] is ...
Došlý, Ondřej
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, 1978 Linear independence of the principal solutions at ∞ and −∞ for identically normal, formally self-adjoint differential systems U′ = AU + BV, V′ = CU − A∗V, with B ⩾ 0, which are disconjugate on (−∞, ∞), is characterized by the condition W−∞ < W∞ on (−∞, ∞)
Ahlbrandt, Calvin D
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Existence and non-existence of sign-changing solutions for a class of two-point boundary value problems involving one-dimensional $p$-Laplacian [PDF]
, 2002 summary:We consider the boundary value problem involving the one dimensional $p$-Laplacian, and establish the precise intervals of the parameter for the existence and non-existence of solutions with prescribed numbers of zeros.
Naito, Yūki +3 more
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, 2006 This work presents a proof of the dependence of the first eigenvalue for uniformly elliptic partial differential equations on the domain in a less abstract setting than that of Ivo Babušhka and Rudolf Výborný in 1965.
Miller, Charles E.
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Methods of oscillation theory of half-linear second order differential equations [PDF]
, 1971 summary:In this paper we investigate oscillatory properties of the second order half-linear equation \[ (r(t)\Phi (y^{\prime }))^{\prime }+c(t)\Phi (y)=0, \quad \Phi (s):= |s|^{p-2}s.
Došlý, Ondřej, Ahlbrandt, Calvin D
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Global asymptotic stability for half-linear differential systems with coefficients of indefinite sign [PDF]
, 2008 summary:This paper is concerned with the global asymptotic stability of the zero solution of the half-linear differential system \[ x^{\prime } = -\,e(t)x + f(t)\phi _{p^*}\!(y)\,,\quad y^{\prime } = -\,g(t)\phi _p(x) - h(t)y\,, \] where $p > 1$, $p ...
Onitsuka, Masakazu, Sugie, Jitsuro
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