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In this paper, we are concerned with the semilinear parabolic equation ∂u/∂t - Δu = g(t,x,u) if $(t, x) \in R_{+} \times Ω$ u = 0 if $(t, x) \in R_{+} \times \partial Ω$ , where $Ω \subset R^{N}$ is a bounded domain with smooth boundary ∂Ω and $g : R_{+} \times \bar{Ω} \times R \to R$ is T-periodic with respect to the first variable. The existence and the multiplicity of T-periodic solutions for this problem are shown when g(t,x,ξ)/ξ lies between two higher eigenvalues of - Δ in Ω with the Dirichlet boundary condition as ξ → ±∞.

Existence of periodic traveling wave solution to the forced generalized nearly concentric Korteweg-de Vries equation.

Jones, Kenneth L., He, Xiaogui, Chen, Yunkai (2000)

International Journal of Mathematics and Mathematical Sciences

Existence of periodic traveling wave solutions to the generalized forced Boussinesq equation.

Jones, Kenneth L., Chen, Yunkai (1999)

International Journal of Mathematics and Mathematical Sciences

Existence of positive and sign-changing solutions for $p$ -Laplace equations with potentials in $ℝ^{N}$ .

Wu, Mingzhu, Yang, Zuodong (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of positive bounded solutions for some nonlinear polyharmonic elliptic systems.

Gontara, Sabrine, El Abidine, Zagharide Zine (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of positive bounded solutions of semilinear elliptic problems.

Toumi, Faten (2010)

International Journal of Differential Equations

Existence of positive radial solutions for a weakly coupled systems via blow up.

García-Huidobro, Marta, Guerra, Ignacio, Manásevich, Raúl (1998)

Abstract and Applied Analysis

Existence of positive radial solutions for the elliptic equations on an exterior domain

Yongxiang Li, Huanhuan Zhang (2016)

Annales Polonici Mathematici

We discuss the existence of positive radial solutions of the semilinear elliptic equation ⎧-Δu = K(|x|)f(u), x ∈ Ω ⎨αu + β ∂u/∂n = 0, x ∈ ∂Ω, ⎩ $l i m_{| x | \to \infty} u (x) = 0$ , where $Ω = x \in ℝ^{N} : | x | > r ₀$ , N ≥ 3, K: [r₀,∞) → ℝ⁺ is continuous and $0 < \int_{r ₀}^{\infty} r K (r) d r < \infty$ , f ∈ C(ℝ⁺,ℝ⁺), f(0) = 0. Under the conditions related to the asymptotic behaviour of f(u)/u at 0 and infinity, the existence of positive radial solutions is obtained. Our conditions are more precise and weaker than the superlinear or sublinear growth conditions. Our discussion is based on the fixed point...

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Existence of infinitely many solutions for elliptic boundary-value problems with nonsymmetrical critical nonlinearity.

Existence of least energy solutions to coupled elliptic systems with critical nonlinearities.

Existence of many positive nonradial solutions for a superlinear Dirichlet problem on thin annuli.

Existence of multiple solutions for a nonlinearly perturbed elliptic parabolic system in $ℝ^{2}$ .

Existence of multiple solutions for a $p (x)$ -Laplace equation.

Existence of nonnegative solutions to positone-type problems in $ℝ^{N}$ with indefinite weights.

Existence of nontrivial solution for a nonlocal elliptic equation with nonlinear boundary condition.

Existence of periodic solutions for semilinear parabolic equations

Existence of periodic traveling wave solution to the forced generalized nearly concentric Korteweg-de Vries equation.

Existence of periodic traveling wave solutions to the generalized forced Boussinesq equation.

Existence of positive and sign-changing solutions for $p$ -Laplace equations with potentials in $ℝ^{N}$ .

Existence of positive bounded solutions for some nonlinear polyharmonic elliptic systems.

Existence of positive bounded solutions of semilinear elliptic problems.

Existence of positive radial solutions for a weakly coupled systems via blow up.

Existence of positive radial solutions for the elliptic equations on an exterior domain

Existence of positive solutions for $p (x)$ -Laplacian problems.

Existence of positive solutions for some Dirichlet problems with an asymptotically homogeneous operator.

Existence of positive solutions for some nonlinear elliptic systems on the half space.

Existence of positive solutions for some nonlinear elliptic problems in unbounded domains of $ℝ^{n}$ .

Existence of positive solutions for some nonlinear parabolic equations in the half space.

Currently displaying 241 – 260 of 366