Laplacian equation
Remark on the Cauchy problem for the evolution p Laplacian equation
... this equation, we first establish the propa- gation estimate and the decay estimate for the solutions of the problem of ...p-Laplacian equation is continuous from the compact set B σ M ,+ to the space ...
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Solutions for a degenerate \(p(x)\)-Laplacian equation with a nonsmooth potential
... p(x)-Laplacian equation with a nonsmooth ...p(x)-Laplacian equation by the theories of nonsmooth critical point and the variable exponent Lebesgue-Sobolev ...
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The boundary value condition of an evolutionary \(p(x)\)-Laplacian equation
... The equation emerges in the so-called electrorheological fluid theory, in which p(x) is as a function of the external electromag- netic field (see [, ] and the references ...p-Laplacian equation and ...
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Multiplicity of solutions for a p-Laplacian equation with nonlinear boundary conditions
... In this paper, we used the three critical points theorem to prove the existence of three distinct solutions for an important clas of boundary value problems associate with p-Laplacian equation. This theorem ...
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A resonant boundary value problem for the fractional p Laplacian equation
... The purpose of this paper is to study the solvability of a resonant boundary value problem for the fractional p-Laplacian equation. By using the continuation theorem of coincidence degree theory, we obtain ...
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On the evolutionary p Laplacian equation with a partial boundary value condition
... is imposed. However, for Eq. (1.6) considered in this paper, since the equations are strongly nonlinear and degenerate, including the extremely case of a ≡ 0, Fichera–Oleˇinik theory is invalid, the corresponding problem ...
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Existence and Nonexistence of Positive Solutions for Singular -Laplacian Equation in
... 10 F. Brock, L. Iturriaga, J. S´anchez, and P. Ubilla, “Existence of positive solutions for p-Laplacian problems with weights,” Communications on Pure and Applied Analysis, vol. 5, no. 4, pp. 941–952, 2006. 11 A. ...
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Lyapunov type inequalities for a fractional p Laplacian equation
... Abstract In this paper, we present new Lyapunov-type inequalities for a fractional boundary value problem that models a turbulent flow in a porous medium.. The obtained inequalities are u[r] ...
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An Introductory View of the Weak Solution of the p Laplacian Equation
... Since we do not know that the weak solution of 1.1 is smooth, later when we prove the main result, we will need to regularise the problem so that a smooth solution exist, in other words,[r] ...
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The stability of evolutionary \(p(x)\)-Laplacian equation
... It implies that the classical solutions (if there are any) of equation (.) are controlled by the initial value completely. Certainly, since equation (.) is degenerate on the boundary and may be ...
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The uniqueness of a nonlinear diffusion equation related to the p Laplacian
... is always necessary. Different from the usual evolutionary p-Laplacian equation or equa- tion (1.1), an obvious feature of equations (1.2), (1.3) lies in that the diffusion coefficient ρ α depends on the ...
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Existence of solutions and nonnegative solutions for a class of p(t)-Laplacian differential systems with multipoint and integral boundary value conditions
... p(t)-Laplacian equation group, there are few papers dealing with the existence of solutions, especially the exis- tence of solutions for the systems with multipoint and integral boundary value ...
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The integral equation methods for the perturbed Helmholtz eigenvalue problems
... integral equation method in the evaluation of eigenfunctions and the corresponding eigenvalues of the two-dimensional Laplacian op- erator under boundary variations of the ...
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Positive periodic solution for ϕ-Laplacian Rayleigh equation with strong singularity
... Rayleigh equation can be derived from many fields, such as the physics, mechanics, and engineering technique fields, and an important question is whether this equation can support periodic ...Rayleigh ...
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On a parabolic equation related to the p-Laplacian
... parabolic equation related to the ...the equation is degenerate on the boundary, no matter we can define the trace of the solution on the boundary or not, by choosing a suitable test function, the stability ...
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General energy decay for nonlinear wave equation of $phi-$Laplacian type with a delay term in the internal feedback
... It is well known that the φ− Laplacian operator degenerates equations in divergence form. It has been much studied during the last years and their results is by now rather developed, especially with delay. In the ...
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On Optimal Control of Quasi-Linear Elliptic Equation with Variable px -Laplacian
... [5] T. Durante, O. P. Kupenko and R. Manzo, ”On attainability of optimal controls in coefficients for system of Hammerstein type with anisotropic p-Laplacian,” Ricerche di Matematica, vol.66, no. 2, pp.259-292, ...
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Existence of Viscosity Solutions to a Parabolic Inhomogeneous Equation Associated with Infinity Laplacian
... They also introduced the corresponding approximating equations and got the uniform continuity estimates of approximate solutions by the barrier function arguments. By this approximate procedure, the existence of the ...
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Positive periodic solution for indefinite singular Liénard equation with p Laplacian
... differential equation with repulsive singularity and, based on Schaefer’s fixed point theorem, new conditions for the existence of periodic solutions were ...
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The stability of the solutions of an equation related to the p-Laplacian with degeneracy on the boundary
... is considered, where ρ (x) = dist(x, ∂ ) is the distance function from the boundary. If α < p – 1, the weak solution belongs to H γ for some γ > 1, the Dirichlet boundary condition can be imposed as usual, the ...
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